Vertical angles are congruent, which means their measures are equal. Given:
- \( m∠2 = (5x + 23)° \)
- \( m∠4 = (3x + 35)° \)
Setting these two expressions equal to each other:
\[ 5x + 23 = 3x + 35 \]
Now, solve for \( x \):
-
Subtract \( 3x \) from both sides: \[ 5x - 3x + 23 = 35 \] \[ 2x + 23 = 35 \]
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Subtract 23 from both sides: \[ 2x = 35 - 23 \] \[ 2x = 12 \]
-
Divide by 2: \[ x = 6 \]
Now, substitute \( x \) back into either angle's measure to find the angle measures. Using \( m∠2 \):
\[ m∠2 = 5(6) + 23 = 30 + 23 = 53° \]
And for \( m∠4 \):
\[ m∠4 = 3(6) + 35 = 18 + 35 = 53° \]
Both angles measure 53°.
Thus, the measure of each angle is 53°.