Question

use this figure to answer the question below. the measure of ∠fih is 90°. what is the measure of ∠gif?

Explanation:

Step1: Set up the equation

Since $\angle FIH = 90^{\circ}$, and $\angle FIG+\angle GIH=\angle FIH$, we have $5x + 4x=90$.

Step2: Solve for $x$

Combine like - terms: $9x = 90$. Divide both sides by 9: $x=\frac{90}{9}=10$.

Step3: Find the measure of $\angle GIF$

Substitute $x = 10$ into $5x$. So, $\angle GIF=5\times10 = 50^{\circ}$.

Answer:

$50^{\circ}$