Answer:
[tex]x=\frac{133}{3}^o[/tex]
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
[tex]m\angle B+2x=180^o[/tex] ----> by supplementary angles (form a linear pair)
[tex]m\angle B=180^o-2x[/tex]
step 2
Find the value of x
Applying the triangle external angle theorem
[tex]86^o+(180-2x)^o=4x^o[/tex]
solve for x
[tex]86^o+(180-2x)^o=4x^o[/tex]
[tex]4x+2x=266\\6x=266[/tex]
[tex]x=\frac{266}{6}^o[/tex]
simplify
[tex]x=\frac{133}{3}^o[/tex]
