Question

if m∠efg = (7x + 101)°, find the requested values.

Explanation:

Step1: Set up equation

Since $\angle EFG=\angle EFH+\angle HFG$, we have $(7x + 101)=(147 - 9x)+(-8x + 122)$.

Step2: Simplify right - hand side

Combine like terms on the right - hand side: $(147 - 9x)+(-8x + 122)=147+122-9x-8x=269 - 17x$. So the equation becomes $7x + 101=269 - 17x$.

Step3: Add $17x$ to both sides

$7x+17x + 101=269-17x+17x$, which simplifies to $24x + 101=269$.

Step4: Subtract 101 from both sides

$24x+101 - 101=269 - 101$, resulting in $24x=168$.

Step5: Solve for $x$

Divide both sides by 24: $x=\frac{168}{24}=4$.

Answer:

$x = 4$