Question

(5x + 2)° y (8x - 25

Explanation:

Step1: Identify vertical angles

The angles \((5x + 2)^\circ\) and \((8x - 25)^\circ\) are vertical angles, so they are equal.
\[5x + 2 = 8x - 25\]

Step2: Solve for \(x\)

Subtract \(5x\) from both sides:
\[2 = 3x - 25\]
Add 25 to both sides:
\[27 = 3x\]
Divide by 3:
\[x = 9\]

Step3: Find the measure of the angle

Substitute \(x = 9\) into \((5x + 2)^\circ\):
\[5(9) + 2 = 45 + 2 = 47^\circ\]

Step4: Find \(y\)

Since there is a right angle (the square symbol), the sum of \((5x + 2)^\circ\), \(y\), and the right angle is \(180^\circ\) (linear pair). The right angle is \(90^\circ\), so:
\[47 + y + 90 = 180\]
\[y + 137 = 180\]
Subtract 137:
\[y = 43\]

Answer:

If we were finding \(x\), \(x = 9\); if finding \(y\), \(y = 43\) (assuming the question is to find \(y\) or \(x\), based on the diagram's context, likely \(x = 9\) and \(y = 43\)). If the question was to solve for \(x\), the answer is \(x = 9\).