Question

Find the angle measure x in the following figures.
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Answer 1

To find:-

The value of x

In the figure:-

Firstly we need to name the figure. Refer to the attachment.

Solution:-

1st case,

$\sf{\angle EAB + \angle BAC = 180^\circ\:\: [Linear\:Pair]}$

= $\sf{125^\circ + \angle BAC = 180^\circ}$

$\sf{\implies \angle BAC = 180^\circ - 125^\circ}$

$\sf{\implies \angle BAC = 55^\circ}$

2nd case,

$\sf{\angle ABC + \angle CBF = 180^\circ\:\:[Linear\:Pair]}$

= $\sf{\angle ABC + 125^\circ = 180^\circ}$

$\sf{\implies \angle ABC = 180^\circ - 125^\circ}$

$\sf{\implies \angle ABC = 55^\circ}$

3rd case,

According To Angle-Sum property of Triangle,

$\sf{\angle ABC + \angle BAC + \angle ACB = 180^\circ}$

= $\sf{55^\circ + 55^\circ + \angle ACB = 180^\circ}$

$\sf{\implies 110^\circ + \angle ACB = 180^\circ}$

$\sf{\implies \angle ACB = 180^\circ - 110^\circ}$

$\sf{\implies \angle ACB = 70^\circ}$

Now,

$\sf{\angle ACB + \angle ACD = 180^\circ\:\:[Linear\:Pair]}$

= $\sf{70^\circ + x = 180^\circ}$

$\sf{\implies x = 180^\circ - 70^\circ}$

$\sf{\implies x = 110^\circ}$

$\sf{\therefore The\:value\:of\:x\:is\:110^\circ}$

Extra Information:-

What is Angle - Sum Property of a triangle?

Answer-> Angle - Sum property of a triangle states that the sum of all the angles of triangle is always 180°.