Question

If in the given figure,p||q and t||r,
find x​

Answer 1

★ How to do :-

Here, we are given with a diagram which has two pairs of parellel lines passing each other. And one of the exterior angle measures 115°. So, on the other side there is other angle named as 'x'. So, we should find the value of that 'x'. To find that first we should find the angle which is opposite to the angle measuring 115°. And then we can find the angle measuring 'x'. So, let's do it!

$\:$

➤ Solution :-

Measurement of angle opposite to 115°

Here we know that vertically opposite angles are always equal to each other. So, that angle also measures the same.

$\tt \leadsto 115 = 115$

Now,

Measurement of 'x' :-

Here we know that the corresponding angles are always equal to each other. So, the angle 'x' also measures the same degrees as obtained in older angle.

$\tt \leadsto \orange{\boxed{\tt \angle{x} = 115^{\circ}}}$

$\Huge\therefore$ The measurement of ∠x is 115°.

━━━━━━━━━━━━━━━━━━━━━━━

More to know :-

• Adjacent angles :- The adjacent angles are those angles which have a common arm and a common vertex i.e, a common ray and a common point.
• Corresponding angles :- The corresponding angles are those angles in which one exterior and one interior of the same side of transversal are equal.
• Vertically opposite angles :- These are the angles in which they have a common point and they lie opposite to each other. They measure equally in degrees.
• Alternate angles :- These are the angles in which both teh angles live in interior but they'll be in opposite, and other pair in which both lives in exterior side.