Question

In each of the following figures, I || p and m is a transversal. Find the values of x, y, and z
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Answer 1

★ How to do :-

Here, we are given with the diagram which consists a pair of lines that are parellel to each other. There is a line passing through that parellel lines. We are given with three variables named as x, y and z. We are asked to find the values of those angles. Here, we are going to use the concepts of alternate angles, corresponding angles, sum of interior angles on same side of transversal. We are also going to use the concept of linear pair of angles, which means they measure 180° totally. So, let's solve!!

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➤ Solution (1) :-

We know that linear pair of angles measure 180° together when added. So,

Value of ∠x :-

${\tt \leadsto \angle{x} + 105 = {180}^{\circ}}$

${\tt \leadsto \angle{x} = 180 - 105}$

${\tt \leadsto \orange{\boxed{\tt \angle{x} = {75}^{\circ}}}}$

We know that alternate angles always measures the same in degrees. So, it measures some as ∠x.

Value of ∠y :-

${\tt \leadsto \orange{\boxed{\tt \angle{y} = {75}^{\circ}}}}$

We know that linear pair of angles measure 180° when added. So,

Value of ∠z :-

${\tt \leadsto 75 + \angle{z} = {180}^{\circ}}$

${\tt \leadsto \angle{z} = 180 - 75}$

${\tt \leadsto \orange{\boxed{\tt \angle{z} = {105}^{\circ}}}}$

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➤ Solution (2) :-

We know that linear pair of angles measure 180° when added. So,

Value of ∠x :-

${\tt \leadsto 75 + \angle{x} = {180}^{\circ}}$

${\tt \leadsto \angle{x} = 180 - 75}$

${\tt \leadsto \orange{\boxed{\tt \angle{x} = {105}^{\circ}}}}$

We know that the sum of the same side of transversal measures 180° when added. So,

Value of ∠y :-

${\tt \leadsto 105 + \angle{y} = {180}^{\circ}}$

${\tt \leadsto \angle{y} = 180 - 105}$

${\tt \leadsto \orange{\boxed{\tt \angle{y} = {75}^{\circ}}}}$

We know that the linear pair of angles measure 180° when added. So,

Value of ∠z :-

${\tt \leadsto 75 + \angle{z} = {180}^{\circ}}$

${\tt \leadsto \angle{z} = 180 - 75}$

${\tt \leadsto \orange{\boxed{\tt \angle{z} = {105}^{\circ}}}}$

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➤ Solution (3) :-

We know that the corresponding angles measure the same in measurements of degrees. So,

Value of ∠x :-

${\tt \leadsto \orange{\boxed{\tt \angle{x} = {110}^{\circ}}}}$

We know that the linear pair of angles measure 180° when added together. So,

Value of ∠y :-

${\tt \leadsto 110 + \angle{y} = {180}^{\circ}}$

${\tt \leadsto \angle{y} = 180 - 110}$

${\tt \leadsto \orange{\boxed{\tt \angle{y} = {70}^{\circ}}}}$

We know that the vertically opposite angles measures same in measurements of degrees. So,

Value of ∠z :-

${\tt \leadsto \orange{\boxed{\tt \angle{z} = {110}^{\circ}}}}$

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Hence solved !!