Question

Calculate the value of X

Answer 1

Answer:

$x=\frac{133}{3}^o$

Step-by-step 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

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

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

$x=\frac{266}{6}^o$

simplify

$x=\frac{133}{3}^o$