Question

the measures of \\( \angle g \\) and \\( \angle h \\) in \\( \triangle fgh \\) are shown.
what is the value of \\( x \\)?
\\( \frac { 20 } { 7 } \\)
9
13
\\( \frac { 73 } { 7 } \\)

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 \(\triangle FGH\), the exterior angle at \(F\) \((7x + 8)^{\circ}\) is equal to the sum of \(\angle H=71^{\circ}\) and \(\angle G = 28^{\circ}\). So, we can write the equation \(7x+8=71 + 28\).

Step2: Simplify the right - hand side of the equation

Calculate \(71+28\).
\(71+28=99\). So the equation becomes \(7x+8 = 99\).

Step3: Solve for \(x\)

Subtract \(8\) from both sides of the equation:
\(7x+8-8=99 - 8\).
\(7x=91\).
Divide both sides by \(7\):
\(x=\frac{91}{7}\).
\(x = 13\).

Answer:

\(13\)