NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

(ii) Let ∠x=63° and ∠y= 27° ∴ ∠x+ ∠y= 63° + 27°= 90°
Hence, ∠x and ∠y are complementary angles. 

(iii) Let ∠x = 112° and y=68° ∴ ∠x+ ∠y=112° + 68° = 180°
Hence, ∠x and ∠y are supplementary angles. 

(iv) Let ∠x= 130° and ∠y = 50 ∴ ∠x+∠y = 130°+50° = 180°
Hence, ∠x and ∠y are supplementary angles. 

(v) Let ∠x=45° and ∠y=45°  ∴ ∠x+ ∠y = 45°+45° = 90
Hence, ∠x and ∠y are complementary angles. 

(vi) Let ∠x=80° and ∠y= 10° ∴  ∠x+ ∠y = 80°+10° = 90°
Hence, ∠x and ∠y are complementary angles.

4. Find the angle which is equal to its complement.

Answer

We know that, two angles are complementary, if their sum is $90^{\circ}$.

We know that, two angles are supplementary, if their sum is $180^{\circ}$.

Let the angle be $x^{\circ}$.

Therefore, its supplement be $180^{\circ}-x^{\circ}$.

Since, the angle is equal to it supplement.

$\therefore \quad x^{\circ}=180^{\circ}-x^{\circ}$

On transposing $x^{\circ}$ from RHS to LHS, we get

$x^{\circ}+x^{\circ}=180^{\circ} \quad \Rightarrow \quad 2 x^{\circ}=180^{\circ}$

We know that, the two angles are supplementary, if their sum is $180^{\circ}$.

$\angle 1+\angle 2=180^{\circ}$ [given]

$\therefore$ Now, if $\angle 1$ is decreased, then $\angle 2$ should be increased, so that both the angles still remain supplementary.

i.e. $\angle 1+\angle 2=180^{\circ}$

We know that, the sum of two complementary angles is $90^{\circ}$, So, if an knele is greater than $45^{\circ}$, then its complementary angle would be less then $45^{\circ}$.

9. In the adjoining figure:
(i) Is ∠1 adjacent to ∠2?
(ii) Is ∠AOC adjacent to ∠AOE?
(iii) Do ∠COE and ∠EOD form a linear pair?
(iv) Are ∠BOD and ∠DOA supplementary?
(v) Is ∠1 vertically opposite to ∠4?
(vi) What is the vertically opposite angle of ∠5?

(i) Yes, $\angle 1$ is adjacent to $\angle 2$ because $\angle 1$ and $\angle 2$ have common vertex $O$. Also, they have a common arm $O C$ and their other arms $O A$ and $O E$ lie on the opposite side of the common arm $O C$.

(ii) No, $\angle A O C$ is not adjacent to $\angle A O E$ because $\angle A O C$ is a part of $\angle A O E$ i.e. they have common interior point $C$.

(iii) Yes, $\angle C O E$ and $\angle E O D$ form a linear pair because $C O D$ is a straight line.

(iv) Yes, $\angle B O D$ and $\angle D O A$ are supplementary because $\angle B O D+\angle D O A=180^{\circ}$.

(v) Yes, $\angle 1$ is vertically opposite to $\angle 4$.

(vi) Vertically opposite angle of $\angle 5$ is $\angle B O C$

$\angle z=\angle y=125^{\circ} \quad$ [vertically opposite angles]

Hence, $\angle x=55^{\circ}, \angle y=125^{\circ}$, and $\angle z=125^{\circ}$

$\begin{array}{ll}\text { (ii) } \angle y+40^{\circ}=180^{\circ} & \text { [by linear pair] }\end{array}$

$\Rightarrow \quad \angle y=180^{\circ}-40^{\circ} \Rightarrow \angle y=140^{\circ}$

$\begin{aligned} \angle z=40^{\circ} & \text { [vertically opposite angles] } \end{aligned}$

(i) If two angles are complementary, then the sum of their measures is _______.
(ii) If two angles are supplementary, then the sum of their measures is ______.
(iii) Two angles forming a linear pair are _______________.
(iv) If two adjacent angles are supplementary, they form a ___________.
(v) If two lines intersect at a point, then the vertically opposite angles are always _____________.
(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are __________.

Answer

(i) If two angles. are complementary, then the sum of their measures is 90°