Question

2.6 In få. 6. if AB || CD, then find L1 and L2 A 2/ B q 75 ris, 6​

Answer 1

★ Correct Question :-

In the given figure AB||CD, then find the measurements of the angles 1 and 2.

★ Solution :-

First, we should find the angles marked as x and y.

We know that the corresponding angles measure the same. So,

$\sf \leadsto x = {75}^{\circ}$

$\sf \leadsto y = {68}^{\circ}$

Now, we can find the values of the first and second angles.

Measurement of first angle :

$\sf \leadsto Straight \: line \: angle = {180}^{\circ}$

$\sf \leadsto y + \angle{1} = {180}^{\circ}$

$\sf \leadsto {68}^{\circ} + \angle{1} = {180}^{\circ}$

$\sf \leadsto \angle{1} = 180 - 68$

$\sf \leadsto \angle{1} = {112}^{\circ}$

Measurement of second angle :

$\sf \leadsto x + \angle{2} = {180}^{\circ}$

$\sf \leadsto {75}^{\circ} + \angle{2} = {180}^{\circ}$

$\sf \leadsto \angle{2} = 180 - 75$

$\sf \leadsto \angle{2} = {105}^{\circ}$

Hence, the values of first and second angle is 112° and 105° respectively.

Answer 2

Question:

In figure, if AB||CD, then find $\angle 1$ and $\angle 2$

Given:

• AB||CD

To Find:

• $\angle 1$
• $\angle 2$

Construction:

To find the $\angle 1$ and $\angle 2$. Let's firstly take $\bold{x}$ and $\bold{y}$ such that $\angle 1$ makes angle of linear pair with $\bold{x}$ and $\angle 2$ such that it makes angle of linear pair with $\bold{y}$.

Solution:

Here We can observe that x and y forms corresponding angle with 68° and 75° respectively. Therefore,

$\hookrightarrow\sf{x={68}^{o}}$

$\hookrightarrow\sf{y={75}^{o}}$

Now, x & y forms angle of linear pair with $\angle 1$ and $\angle 2$ respectively. So, By linear pair. We get,

$\rightarrow\mathsf{x+\angle 1={180}^{o}}$

$\rightarrow\mathsf{{68}^{o}+\angle 1={180}^{o}}$

$\rightarrow\mathsf{\angle 1={180}^{o}-{68}^{o}}$

$\rightarrow\mathsf{\angle 1={112}^{o}}$

Also,

$\rightarrow\mathsf{y+\angle 2={180}^{o}}$

$\rightarrow\mathsf{{75}^{o}+\angle 2={180}^{o}}$

$\rightarrow\mathsf{\angle 2={180}^{o}-{75}^{o}}$

$\rightarrow\mathsf{\angle 2={105}^{o}}$

Final Answer:

Hence, values of $\angle 1$ and $\angle 2$ are 112° and 105° respectively.