Vertical angles are equal, so you can set the measures of the two angles equal to each other:
\[ m∠2 = m∠4 \]
Substituting in the expressions for the angles:
\[ 5x + 23 = 3x + 35 \]
Now, solve for \(x\):
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Subtract \(3x\) from both sides: \[ 5x - 3x + 23 = 35 \] \[ 2x + 23 = 35 \]
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Subtract \(23\) from both sides: \[ 2x = 35 - 23 \] \[ 2x = 12 \]
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Divide by \(2\): \[ x = 6 \]
Now, substitute \(x\) back into either angle to find the measures:
For \(m∠2\): \[ m∠2 = 5(6) + 23 = 30 + 23 = 53° \]
For \(m∠4\): \[ m∠4 = 3(6) + 35 = 18 + 35 = 53° \]
Thus, both angles measure \(53°\).
The measure of each angle is 53 degrees.
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