Question

in the triangle below, ∠g is a right angle. suppose that m∠f=(4x+24)° and m∠h=(2x+18)°.
(a) write an equation to find x. make sure you use an \=\ sign in your answer.
equation:
(b) find the degree measure of each angle.
m∠f= °
m∠g= °
m∠h= °

Explanation:

Step1: Sum angles to 180°

The sum of angles in a triangle is $180^\circ$, with $\angle G = 90^\circ$.
$$(4x+24) + (2x+18) + 90 = 180$$
Simplify the left side:
$$6x + 132 = 180$$

Step2: Solve for x

Subtract 132 from both sides:
$$6x = 180 - 132$$
$$6x = 48$$
Divide by 6:
$$x = \frac{48}{6} = 8$$

Step3: Calculate $\angle F$

Substitute $x=8$ into $\angle F$ expression:
$$m\angle F = 4(8) + 24 = 32 + 24 = 56$$

Step4: Confirm $\angle G$

$\angle G$ is a right angle:
$$m\angle G = 90$$

Step5: Calculate $\angle H$

Substitute $x=8$ into $\angle H$ expression:
$$m\angle H = 2(8) + 18 = 16 + 18 = 34$$

Answer:

(a) Equation:

$6x + 132 = 180$

(b) Angle measures:

$m\angle F = 56^\circ$
$m\angle G = 90^\circ$
$m\angle H = 34^\circ$