Question

the measures of $\angle x$ and $\angle y$ are equal. which is the value of $m$?
$3(m + 2)$ $5m - 58$
$m = 8$
$m = 26$
$m = 30$
$m = 32$

Explanation:

Step1: Set the expressions equal

Since \( \angle x \) and \( \angle y \) are equal, their expressions \( 3(m + 2) \) and \( 5m - 58 \) are equal. So we set up the equation:
\( 3(m + 2) = 5m - 58 \)

Step2: Expand the left side

Using the distributive property, \( 3(m + 2) = 3m + 6 \). Now the equation is:
\( 3m + 6 = 5m - 58 \)

Step3: Subtract \( 3m \) from both sides

\( 6 = 2m - 58 \)

Step4: Add 58 to both sides

\( 6 + 58 = 2m \)
\( 64 = 2m \)

Step5: Divide both sides by 2

\( m = \frac{64}{2} = 32 \)

Answer:

\( m = 32 \)