We can see that the measures of the interior angles are (x+8)^(∘) and 4x^(∘). According to the Exterior Angle Theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. This allows us to write an equation.
7x-16=(x+8)+4x
We will now solve the above equation for x.
Now we can substitute x= 12 in the expression 7x-16 to find the measure of the angle.
7( 12)-16=68^(∘)
Therefore, the measure of the exterior angle is 68^(∘).
