Question

Find the values of x & y in the following figure.

Answer 1

please check the answer

Answer 2

★ How to do :-

Here, we are given with a diagram consisting of a triangle with an exterior angle. We are provided with one of the angle of triangle in it's interior as 50° and the other angle's measurement is given which is in exterior of the triangle as 80°. We are given with two variables x and y, in which we are asked to find the value of those. Here, we are going to use the concepts of vertically opposite angles and the triangle aum property which are explained while solving. So, let's solve!!

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➤ Solution :-

We know that the vertically opposite angles are equal. So, the angle y will measure the same as it's other vertical angle. So,

Value of ∠y :-

${\tt \leadsto {80}^{\circ} = y}$

${\tt \leadsto \orange{\underline{\boxed{ \tt y = {80}^{\circ}}}}}$

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We know that all the angles of a triangle when added together should result in 180. So,

Value of ∠x :-

${\tt \leadsto 50 + 80 + x = 180}$

Add the given numbers.

${\tt \leadsto 130 + x = 180}$

Shift the number in LHS to the side of RHS.

${\tt \leadsto x = 180 - 130}$

Add the values to find x.

${\tt \leadsto \orange{\underline{\boxed{ \tt x = {50}^{\circ}}}}}$

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More to know :-

• The vertically opposite angles are always equal to each other. They are formed when two lines intersect each other. There are two pairs of vertically opposite angles in a pair of intersecting lines.
• All the angles of a triangle will always result in 180° when added together. If they don't result in 180, then they cannot form a triangle. It's also known as angle sum property.