Question

1. given that ∠efg is a right angle, find m∠efh and m∠hfg.

Explanation:

Step1: Set up equation based on angle - sum

Since $\angle EFG$ is a right - angle ($90^{\circ}$) and $\angle EFG=\angle EFH+\angle HFG$, we have the equation $(2x + 2)+(x + 1)=90$.

Step2: Combine like terms

Combining the left - hand side of the equation: $2x+x+2 + 1=90$, which simplifies to $3x+3 = 90$.

Step3: Solve for $x$

Subtract 3 from both sides: $3x=90 - 3=87$. Then divide both sides by 3: $x=\frac{87}{3}=29$.

Step4: Find $\angle EFH$

Substitute $x = 29$ into the expression for $\angle EFH$: $\angle EFH=2x + 2=2\times29+2=58 + 2=60^{\circ}$.

Step5: Find $\angle HFG$

Substitute $x = 29$ into the expression for $\angle HFG$: $\angle HFG=x + 1=29+1=30^{\circ}$.

Answer:

$m\angle EFH = 60^{\circ}$, $m\angle HFG = 30^{\circ}$