Question

find the measure of the exterior angle shown. exterior angle =

Explanation:

Step1: Apply exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. So, we set up the equation $6x - 7=2x+(103 - x)$.

Step2: Simplify the right - hand side of the equation

Combine like terms on the right - hand side: $2x+(103 - x)=2x + 103-x=x + 103$. So the equation becomes $6x-7=x + 103$.

Step3: Solve for $x$

Subtract $x$ from both sides: $6x-x-7=x-x + 103$, which simplifies to $5x-7 = 103$. Then add 7 to both sides: $5x-7 + 7=103 + 7$, so $5x=110$. Divide both sides by 5: $x=\frac{110}{5}=22$.

Step4: Find the measure of the exterior angle

Substitute $x = 22$ into the expression for the exterior angle $6x-7$. So, $6(22)-7=132-7 = 125$.

Answer:

$125$