Question

the measures of ∠g and ∠h in △fgh are shown. what is the value of x? 20/7 9 12

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In \(\triangle FGH\), \((7x + 8)^{\circ}=71^{\circ}+28^{\circ}\)

Step2: Simplify the right - hand side

\(71^{\circ}+28^{\circ}=99^{\circ}\), so the equation becomes \(7x + 8=99\)

Step3: Solve for \(x\)

Subtract \(8\) from both sides: \(7x=99 - 8\), \(7x=91\). Then divide both sides by \(7\): \(x=\frac{91}{7}=13\)

Answer:

\(13\)