Vertical angles are equal, so we can set the expressions for the angles equal to each other:
\[ m∠2 = m∠4 \]
This gives us the equation:
\[ 5x + 23 = 3x + 35 \]
Now, we can 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, we can substitute \( x \) back into either angle measure to find the measure of the angles:
Using \( m∠2 = 5x + 23 \): \[ m∠2 = 5(6) + 23 = 30 + 23 = 53° \]
Using \( m∠4 = 3x + 35 \): \[ m∠4 = 3(6) + 35 = 18 + 35 = 53° \]
So, both angles measure \( 53° \).
The measure of each angle is 53°.
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