Question

find missing angles quick check (1 point) there are two supplementary angles, ∠d and ∠e, where ( mangle d=(4x + 8)^circ ), and ( mangle e=(x + 17)^circ ), and ( angle f ) is a vertical angle with ( angle d ), what is the measure of ( angle f )? options: 124, 132, 48, 31

Explanation:

Step1: Set up supplementary angle equation

Supplementary angles sum to $180^\circ$, so:
$$(4x + 8) + (x + 17) = 180$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$:
$$5x + 25 = 180$$
$$5x = 155$$
$$x = 31$$

Step3: Calculate $m\angle D$

Substitute $x=31$ into $\angle D$'s expression:
$$m\angle D = 4(31) + 8 = 124 + 8 = 132^\circ$$

Step4: Use vertical angle property

Vertical angles are congruent, so $m\angle F = m\angle D$.

Answer:

C. $132^\circ$