Question

Calculate the value of X

Answer 1

`x=(133)/(3)^o`

Explanation:

The Triangle external angle theorem states that :An exterior angle of a triangle is equal to the sum of the opposite interior angles. For more on this see

see the attached figure with letter to better understand the problem

step 1

Find the measure of the interior angle at B

we know that

`m\angle B+2x=180^o` ----> by supplementary angles (form a linear pair)

`m\angle B=180^o-2x`

step 2

Find the value of x

Applying the triangle external angle theorem

`86^o+(180-2x)^o=4x^o`

solve for x

`86^o+(180-2x)^o=4x^o`

`4x+2x=266\\6x=266`

`x=(266)/(6)^o`

simplify

`x=(133)/(3)^o`