Question

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

image of angle with e (top), f (vertex), g (right), h (between e and g); ∠efh labeled (2x + 2)°, ∠hfg labeled (x + 1)°
m∠efh = □°, m∠hfg = □°

Explanation:

Step1: Set up the equation

Since $\angle EFG$ is a right angle, its measure is $90^\circ$. The sum of $\angle EFH$ and $\angle HFG$ should equal $90^\circ$. So we have the equation:
$$(2x + 2) + (x + 1) = 90$$

Step2: Solve for x

Combine like terms:
$$3x + 3 = 90$$
Subtract 3 from both sides:
$$3x = 87$$
Divide both sides by 3:
$$x = 29$$

Step3: Find $m\angle EFH$

Substitute $x = 29$ into the expression for $\angle EFH$:
$$2x + 2 = 2(29) + 2 = 58 + 2 = 60$$

Step4: Find $m\angle HFG$

Substitute $x = 29$ into the expression for $\angle HFG$:
$$x + 1 = 29 + 1 = 30$$

Answer:

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