Question

determine the measure in degrees of the angle indicated with an arc.
11.
12.

Explanation:

Step1: Solve for \(x\) in problem 11

The sum of angles on a straight line is \(180^{\circ}\). So, \(2x + 82.5+3x=180\).
Combine like - terms: \(5x+82.5 = 180\).
Subtract \(82.5\) from both sides: \(5x=180 - 82.5=97.5\).
Divide by \(5\): \(x=\frac{97.5}{5}=19.5\).
The angle \(2x\) is \(2\times19.5 = 39^{\circ}\).

Step2: Solve for \(x\) in problem 12

The sum of angles around a right - angle (excluding the \(90^{\circ}\) angle) is \(90^{\circ}\). So, \(7x + 8x=90\).
Combine like - terms: \(15x=90\).
Divide by \(15\): \(x = 6\).
The angle \(7x\) is \(7\times6=42^{\circ}\).

Answer:

1. \(39^{\circ}\)
2. \(42^{\circ}\)