Question

question 32 module 7 practice test
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mr. foster installed the gate shown. if $m\angle1 = (3x + 25)^\circ$ and $m\angle4 = (2x)^\circ$, what is $m\angle2$?

Explanation:

Step1: Identify supplementary angles

$\angle 1$ and $\angle 4$ are same-side interior angles, so they are supplementary:
$$(3x + 25) + 2x = 180$$

Step2: Solve for $x$

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

Step3: Find $m\angle 4$

Substitute $x=31$ into $\angle 4$'s expression:
$$m\angle 4 = 2(31) = 62^\circ$$

Step4: Relate $\angle 2$ and $\angle 4$

$\angle 2$ and $\angle 4$ are vertical angles, so they are congruent:
$$m\angle 2 = m\angle 4$$

Answer:

$62^\circ$