# NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles (EX 5.1) Exercise 5.1

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Lines and Angles are covered in Chapter 5 of the NCERT textbook for Class 7. Class 7 Maths Exercise 5.1 is based on some of the basic concepts of Lines and Angles. It covers various important concepts like Complementary and Supplementary Angles, Adjacent Angles, Linear Pair, etc. Along with other study materials offered by Extramarks, the NCERT Solutions For Class 7 Maths Chapter 5 Exercise 5.1 cover all of the key ideas given in the CBSE syllabus for the Class 7 exams. Expert teachers created the NCERT Solutions For Class 7 Maths Chapter 5 Exercise 5.1 to help students be ready for questions found in CBSE Class 7 exams. Students can prepare for a variety of competitive exams like, the Olympiads, by practising the NCERT Solutions For Class 7 Maths Chapter 5 Exercise 5.1. To become proficient with the problems, students should practise the NCERT Solutions for Class 7 Maths Chapter 5 Exercise 5.1 several times.In order to finish the exam question paper within the allotted time, students should practise the NCERT textbook exercises regularly. Their inability to finish the question paper within the allotted time is frequently caused by a lack of practise. The exam paper also has a number of NCERT book-related questions. Students who have access to the NCERT Solutions For Class 7 Maths Chapter 5 Exercise 5.1 learn how to formulate their answers so that they can finish the question paper within the time limit

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**NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles (EX 5.1) Exercise 5.1 **

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**Access NCERT Solutions for class 7 Maths Chapter 5 – Lines And Angles**

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**NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Exercise 5.1**

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**NCERT Solutions for Class 7**

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**Q.1 **

$\mathrm{Find}\mathrm{the}\mathrm{complement}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{angles}:$

**Ans.**

\begin{array}{l}\text{(i) 20}\xb0\\ \text{Since the sum of complementary angle is 90}\xb0\\ \text{So, we have}\\ \text{Complement}=\text{90}\xb0-20\xb0=\overline{)70\xb0}\\ \text{(ii) 63}\xb0\\ \text{Since the sum of complementary angle is 90}\xb0\\ \text{So, we have}\\ \text{Complement}=\text{90}\xb0-63\xb0=\overline{)27\xb0}\\ \text{(iii) 57}\xb0\\ \text{Since the sum of complementary angle is 90}\xb0\\ \text{So, we have}\\ \text{Complement}=\text{90}\xb0-57\xb0=\overline{)33\xb0}\end{array}

**Q.2 **Find the supplement of the following angles:

**Ans.**

\begin{array}{l}\text{(i) 105}\xb0\\ \text{Since the sum of supplementary angle is 180}\xb0\\ \text{So, we have}\\ \text{Complement}=\text{180}\xb0-105\xb0=\overline{)75\xb0}\\ \text{(ii) 87}\xb0\\ \text{Since the sum of Supplementary angle is 180}\xb0\\ \text{So, we have}\\ \text{Complement}=\text{180}\xb0-87\xb0=\overline{)93\xb0}\text{(iii) 154}\xb0\\ \text{Since the sum of Supplementary angle is 180}\xb0\\ \text{So, we have}\\ \text{Complement}=\text{180}\xb0-154\xb0=\overline{)26\xb0}\end{array}

**Q.3 **

$\begin{array}{l}\mathrm{Identify}\mathrm{which}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{pairs}\mathrm{of}\mathrm{angles}\mathrm{aren}\\ \mathrm{complementary}\mathrm{and}\mathrm{which}\mathrm{are}\mathrm{supplementary}.\\ \left(\mathrm{i}\right)65\xb0,115\xb0\left(\mathrm{ii}\right)63\xb0,27\xb0\left(\mathrm{iii}\right)112\xb0,68\xb0\\ \left(\mathrm{iv}\right)130\xb0,50\xb0\left(\mathrm{v}\right)45\xb0,45\xb0\left(\mathrm{vi}\right)80\xb0,10\xb0\end{array}$

**Ans.**

$\begin{array}{l}\left(\text{i}\right)\text{65}\xb0,\text{115}\xb0\\ \text{Since, the sum of complementary angle is 90}\xb0\text{and sum of}\\ \text{supplementary angle is 180}\xb0.\\ \text{So,}65\xb0\text{+115}\xb0=180\xb0\\ \text{Therefore, given pair is supplemenatry}\text{.}\\ \left(\text{ii}\right)\text{63}\xb0,\text{27}\xb0\\ \text{Since, the sum of complementary angle is 90}\xb0\text{and sum of}\\ \text{supplementary angle is 180}\xb0.\\ \text{So,}63\xb0\text{+27}\xb0=90\xb0\\ \text{Therefore, given pair is complementary}\text{.}\\ \left(\text{iii}\right)\text{112}\xb0,\text{68}\xb0\\ \text{Since, the sum of complementary angle is 90}\xb0\text{and sum of}\\ \text{supplementary angle is 180}\xb0.\\ \text{So,}112\xb0\text{+68}\xb0=180\xb0\\ \text{Therefore, given pair is supplemenatry}\text{.}\\ \left(\text{iv}\right)\text{130}\xb0,\text{50}\xb0\\ \text{Since, the sum of complementary angle is 90}\xb0\text{and sum of}\\ \text{supplementary angle is 180}\xb0.\\ \text{So,}130\xb0\text{+50}\xb0=180\xb0\\ \text{Therefore, given pair is supplemenatry}\text{.}\\ \left(\text{v}\right)\text{45}\xb0,\text{45}\xb0\\ \text{Since, the sum of complementary angle is 90}\xb0\text{and sum of}\\ \text{supplementary angle is 180}\xb0.\\ \text{So,}45\xb0\text{+45}\xb0=90\xb0\\ \text{Therefore, given pair is complementary}\text{.}\\ \left(\text{vi}\right)\text{80}\xb0,\text{10}\xb0\\ \text{Since, the sum of complementary angle is 90}\xb0\text{and sum of}\\ \text{supplementary angle is 180}\xb0.\\ \text{So,}80\xb0\text{+10}\xb0=90\xb0\\ \text{Therefore, given pair is complementary}\text{.}\end{array}$

**Q.4 **

$\mathrm{Find}\mathrm{the}\mathrm{angle}\mathrm{which}\mathrm{is}\mathrm{equal}\mathrm{to}\mathrm{its}\mathrm{complement}.$

**Ans.**

$\begin{array}{l}\text{Let the angle be}\mathrm{x}.\\ \text{Since, it also equal to its complement.}\\ \text{So, complement angle}=\text{}\mathrm{x}.\\ \text{Sum of complementary angle is 90}\xb0\\ \text{So, we get}\\ \mathrm{x}+\mathrm{x}=90\xb0\\ 2\mathrm{x}=90\xb0\\ \mathrm{x}=\frac{90\xb0}{2}=45\xb0\\ \text{Thus, the angle be}\overline{)\text{45}\xb0}.\end{array}$

**Q.5 **

$\mathrm{Find}\mathrm{the}\mathrm{angle}\mathrm{which}\mathrm{is}\mathrm{equal}\mathrm{to}\mathrm{its}\mathrm{supplement}.$

**Ans.**

$\begin{array}{l}\text{Let the angle be}\mathrm{x}\text{.}\\ \text{Since, it also equal to its supplement.}\\ \text{So, supplement angle}=\text{}\mathrm{x}\text{.}\\ \text{Sum of supplementary angle is 180}\xb0\\ \text{So, we get}\\ \mathrm{x}+\mathrm{x}=180\xb0\\ 2\mathrm{x}=180\xb0\\ \mathrm{x}=\frac{180\xb0}{2}=90\xb0\\ \text{Thus, the angle be}\overline{)\text{90}\xb0}.\end{array}$

**Q.6 **

$\begin{array}{l}\mathrm{In}\mathrm{the}\mathrm{given}\mathrm{figure},\angle 1\mathrm{and}\angle 2\mathrm{are}\mathrm{supplementary}\mathrm{angles}.\\ \mathrm{If}\angle 1\mathrm{is}\mathrm{decreased},\mathrm{what}\mathrm{changes}\mathrm{should}\mathrm{take}\mathrm{place}\mathrm{in}\angle 2\mathrm{so}\\ \mathrm{that}\mathrm{both}\mathrm{angles}\mathrm{still}\mathrm{remain}\mathrm{supplementary}.\end{array}$

**Ans.**

\begin{array}{l}\text{Since,}\text{\hspace{0.17em}}\angle 1\text{and}\angle 2\text{\hspace{0.17em}}\text{are supplementary angles}\text{.}\\ \text{If}\angle 1\text{\hspace{0.17em}}\text{reduced, then}\angle 2\text{should be increased by the same}\\ \text{measure so that this angle remain supplementary}\text{.}\end{array}

**Q.7 **

$\begin{array}{l}\mathrm{Can}\mathrm{two}\mathrm{angles}\mathrm{be}\mathrm{supplementary}\mathrm{if}\mathrm{both}\mathrm{of}\mathrm{them}\mathrm{are}\\ \left(\mathrm{i}\right)\mathrm{acute}?\\ \left(\mathrm{ii}\right)\mathrm{obtuse}?\\ \left(\mathrm{iii}\right)\mathrm{right}?\end{array}$

**Ans.**

$\begin{array}{l}\text{(i) No, if both angles are acute, that means that both angles}\\ \text{are less than 90}\xb0\text{. In that case, their sum can not be equal to 180}\xb0.\\ \\ \text{(ii) No, if both angles are obtuse, that means that both angles}\\ \text{greater than 90}\xb0.\text{In that case, their sum will exceed 180}\xb0.\\ \\ \text{(iii) Yes, if both angles are right angles, that is, 90}\xb0,\text{\hspace{0.17em}}\text{then their}\\ \text{sum will be exact 180}\xb0.\end{array}$

**Q.8 **An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45°?

**Ans.**

$\begin{array}{l}\text{Let}\mathrm{x}\text{and}\mathrm{y}\text{be two angles having complementary angle pair}\\ \text{and}\mathrm{x}\text{is greater than 45}\xb0.\\ \text{Then,}\\ \mathrm{x}+\mathrm{y}=90\xb0\\ \mathrm{y}=90\xb0-\mathrm{x}\\ \text{Thus, y will be less than 45}\xb0.\end{array}$

**Q.9 **

$\begin{array}{l}\mathrm{In}\mathrm{the}\mathrm{adjoining}\mathrm{figure}:\\ \left(\mathrm{i}\right)\mathrm{Is}\angle 1\mathrm{adjacent}\mathrm{to}\angle 2?\\ \left(\mathrm{ii}\right)\mathrm{Is}\angle \mathrm{AOC}\text{\hspace{0.17em}}\mathrm{adjacent}\mathrm{to}\angle \mathrm{AOE}?\\ \left(\mathrm{iii}\right)\mathrm{Do}\angle \mathrm{COE}\text{\hspace{0.17em}}\mathrm{and}\text{\hspace{0.17em}}\angle \mathrm{EOD}\text{\hspace{0.17em}}\mathrm{form}\mathrm{a}\mathrm{linear}\mathrm{pair}?\\ \left(\mathrm{iv}\right)\mathrm{Are}\angle \mathrm{BOD}\mathrm{and}\text{\hspace{0.17em}}\angle \mathrm{DOA}\text{\hspace{0.17em}}\mathrm{supplementary}?\\ \left(\mathrm{v}\right)\mathrm{Is}\angle 1\mathrm{vertically}\mathrm{opposite}\mathrm{to}\angle 4?\\ \left(\mathrm{v}\right)\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{vertically}\mathrm{opposite}\mathrm{angle}\mathrm{of}\angle 5?\end{array}$

**Ans.**

\begin{array}{l}\text{(i) Yes, since they have a common vetex O and also a common}\\ \text{arm OC}\text{. Also, their non-common arms, OA}\text{}\text{and OB are on}\\ \text{either side of the common arm}\text{.}\\ \text{(ii) No}\text{. they have a common vertex O and also a common}\\ \text{arm OA}\text{. However, their non common arms, OC and OE are on}\\ \text{the same side of the common arm}\text{. Therefore, theses are not}\\ \text{adjacent to each other}\text{.}\\ \text{(iii) Yes, since they have a common vertex O and a common}\\ \text{arm OE}\text{. Also, their non common arms OC and OD, are}\\ \text{opposite rays}\text{.}\\ \text{(iv) Yes, since}\angle \text{BOD and}\angle \text{DOA have a common vertex O and}\\ \text{their non-common arms opposite to each other}\text{.}\\ \text{(v) Yes, since these are fromed dure to the intersection of two}\\ \text{straight lines (AB and CD)}\\ \text{(vi)}\angle \text{COB is the vertically opposite angle of}\angle 5\text{as these are}\\ \text{formed due to the intersection of two straight lines AB and CD}\text{.}\end{array}

**Q.10 **

$\begin{array}{l}\mathrm{Indicate}\mathrm{which}\mathrm{pairs}\mathrm{of}\mathrm{angles}\mathrm{are}:\\ \left(\mathrm{i}\right)\mathrm{Vertically}\mathrm{opposite}\mathrm{angles}.\\ \left(\mathrm{ii}\right)\mathrm{Linear}\mathrm{pairs}.\end{array}$

**Ans.**

\begin{array}{l}\text{(i)}\angle 1\text{,}\angle 4\text{\hspace{0.17em}}\text{and}\angle 5,\text{}\left(\angle 2+\angle 3\right)\text{are vertically opposite angles}\\ \text{as these formed due to the intersection of straight lines}\\ \text{(ii)}\angle 1\text{and}\angle \text{5,}\angle 5\text{\hspace{0.17em}}\text{and,}\angle 4\text{as these have common vertex}\\ \text{and also have non-common arms opposite to each other}\text{.}\end{array}

**Q.11 **In the following figure, is

$\angle 1$

adjacent to

$\angle 2$

**? Give reasons.**

**Ans. **

$\angle 1$

and

$\angle 2$

are not adjacent angles because they don’t have common vertex.

**Q.12 **

**Ans.**

$\begin{array}{l}\text{(i) Since}\angle \mathrm{x}\text{\hspace{0.17em}and}\angle 55\xb0\text{are vertically opposite angles.}\\ \text{So,}\mathrm{x}=\angle 55\xb0\\ \angle \mathrm{x}\xb0+\angle \mathrm{y}\xb0=\angle 180\xb0\\ \angle 55\xb0+\angle \mathrm{y}\xb0=\angle 180\xb0\\ \angle \mathrm{y}\xb0=\angle 180\xb0-\angle 55\xb0\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\angle 125\xb0\\ \angle \mathrm{y}\xb0=\angle \mathrm{z}\xb0\left(\text{vertically\hspace{0.17em}opposite\hspace{0.17em}angles}\right)\\ \mathrm{So},\text{\hspace{0.17em}}\angle \mathrm{z}\xb0=\angle 125\xb0\\ \text{(ii)}\angle \mathrm{z}\xb0=\angle 40\xb0\left(\text{vertically\hspace{0.17em}opposite\hspace{0.17em}angles}\right)\\ \angle \mathrm{y}\xb0+\angle \mathrm{z}\xb0=\angle 180\xb0\left(\text{Linear pair}\right)\\ \angle \mathrm{y}\xb0=\angle 180\xb0-\angle 40\xb0\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\angle 140\xb0\\ \angle 40\xb0+\angle \mathrm{x}\xb0+\angle 25\xb0=\angle 180\xb0\\ \angle \mathrm{x}\xb0+\angle 65\xb0=\angle 180\xb0\\ \angle \mathrm{x}\xb0=\angle 180\xb0-\angle 65\xb0\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\angle 115\xb0\end{array}$

**Q.13 **

$\begin{array}{l}\mathrm{Fill}\mathrm{in}\mathrm{the}\mathrm{blanks}:\\ \left(\mathrm{i}\right)\mathrm{If}\mathrm{two}\mathrm{angles}\mathrm{are}\mathrm{complementary},\mathrm{then}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{their}\\ \mathrm{measures\; is}\_\_\_\_\_\_.\\ \left(\mathrm{ii}\right)\mathrm{If}\mathrm{two}\mathrm{angles}\mathrm{are}\mathrm{supplementary},\mathrm{then}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{their}\\ \mathrm{measures\; is}\_\_\_\_\_.\\ \left(\mathrm{iii}\right)\mathrm{Two}\mathrm{angles}\mathrm{forming}\mathrm{a}\mathrm{linear}\mathrm{pair}\mathrm{are}\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.\\ \left(\mathrm{iv}\right)\mathrm{If}\mathrm{two}\mathrm{adjacent}\mathrm{angles}\mathrm{are}\mathrm{supplementary},\mathrm{they}\mathrm{form}\mathrm{a}\_\_\_\_\_\_\_\_\_\_.\\ \left(\mathrm{v}\right)\mathrm{If}\mathrm{two}\mathrm{lines}\mathrm{intersect}\mathrm{at}\mathrm{a}\mathrm{point},\mathrm{then}\mathrm{the}\mathrm{vertically}\mathrm{opposite}\\ \begin{array}{l}\mathrm{angles}\mathrm{are}\mathrm{always}\_\_\_\_\_\_\_\_\_\_\_\_\_.\\ \begin{array}{l}\left(\mathrm{vi}\right)\mathrm{If}\mathrm{two}\mathrm{lines}\mathrm{intersect}\mathrm{at}\mathrm{a}\mathrm{point},\mathrm{and}\mathrm{if}\mathrm{one}\mathrm{pair}\mathrm{of}\\ \mathrm{vertically}\mathrm{opposite}\mathrm{angles}\mathrm{are}\mathrm{acute}\mathrm{angles},\mathrm{then}\mathrm{the}\\ \mathrm{other}\mathrm{pair}\mathrm{of}\mathrm{vertically}\mathrm{opposite}\mathrm{angles}\mathrm{are}\_\_\_\_\_\_\_\_\_\_.\end{array}\end{array}\end{array}$

**Ans.**

\begin{array}{l}\text{Fill in the blanks}:\\ \left(\text{i}\right)\text{If two angles are complementary},\text{then the sum of their}\\ \text{measures is}\overline{)\text{90}\xb0}.\\ \left(\text{ii}\right)\text{If two angles are supplementary},\text{then the sum of their}\\ \text{measures is}\overline{)180\xb0}.\\ \left(\text{iii}\right)\text{Two angles forming a linear pair are}\overline{)\text{supplementary}}.\\ \left(\text{iv}\right)\text{If two adjacent angles are supplementary},\text{they}\\ \text{form a}\overline{)\text{Linear pair}}.\\ \left(\text{v}\right)\text{If two lines intersect at a point},\text{then the vertically opposite}\\ \text{angles are always}\overline{)\text{equal}}\text{}.\\ \left(\text{vi}\right)\text{If two lines intersect at a point},\text{and if one pair of vertically}\\ \text{opposite angles are acute angles},\text{then the other pair of}\\ \text{vertically opposite angles are}\overline{)\text{obtuse angles}}.\end{array}

**Q.14 **

$\begin{array}{l}\mathrm{In}\mathrm{the}\mathrm{adjoining}\mathrm{figure},\mathrm{name}\mathrm{the}\mathrm{following}\mathrm{pairs}\mathrm{of}\mathrm{angle}.\\ \left(\mathrm{i}\right)\mathrm{Obtuse}\mathrm{vertically}\mathrm{opposite}\mathrm{angles}\\ \left(\mathrm{ii}\right)\mathrm{Adjacent}\mathrm{complementary}\mathrm{angles}\\ \left(\mathrm{iii}\right)\mathrm{Equal}\mathrm{supplementary}\mathrm{angles}\\ \left(\mathrm{iv}\right)\mathrm{Unequal}\mathrm{supplementary}\mathrm{angles}\\ \left(\mathrm{v}\right)\mathrm{Adjacent}\mathrm{angles}\mathrm{that}\mathrm{do}\mathrm{not}\mathrm{form}\mathrm{a}\mathrm{linear}\mathrm{pair}.\end{array}$

**Ans.**

$\begin{array}{l}\text{(i)}\angle \text{AOD},\text{\hspace{0.17em}}\angle \text{BOC}\\ \text{(ii)}\angle \text{EOA},\text{\hspace{0.17em}}\angle \text{AOB}\\ \text{(iii)}\text{\hspace{0.17em}}\angle \text{EOB},\text{\hspace{0.17em}}\angle \text{EOD}\\ \text{(iv)}\text{\hspace{0.17em}}\angle \text{EOA},\text{\hspace{0.17em}}\angle \text{EOC}\\ \text{(v)}\text{\hspace{0.17em}}\angle \text{AOB}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\angle \text{AOE},\text{\hspace{0.17em}}\angle \text{AOE}\text{\hspace{0.17em} and}\text{\hspace{0.17em}}\angle \text{EOD},\text{\hspace{0.17em}}\angle \text{EOD}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\angle \text{COD}\text{.}\end{array}$

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### 2. How many questions are there in NCERT Solutions For Class 7 Maths Chapter 5 Exercise 5.1?

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