Question

question 5 (1 point) using the following diagram and the information provided, find the indicated angle measure. m∠ehg = 77° m∠fhg = ______ blank 1:

Explanation:

Step1: Set up an equation

Since $\angle EHG=\angle EHF+\angle FHG$, we have $(9x + 3)+(13x-25)=77$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $(9x+13x)+(3 - 25)=77$, which simplifies to $22x-22 = 77$.

Step3: Solve for $x$

Add 22 to both sides of the equation: $22x-22 + 22=77 + 22$, so $22x=99$. Then divide both sides by 22: $x=\frac{99}{22}=\frac{9}{2}=4.5$.

Step4: Find $\angle FHG$

Substitute $x = 4.5$ into the expression for $\angle FHG$ which is $13x-25$. So $m\angle FHG=13\times4.5-25=58.5 - 25=33.5^{\circ}$.

Answer:

$33.5^{\circ}$