Question

warm - up
(3x + 28)°
(9y + 4)° 63° (11y - 14)°

Explanation:

Step1: Solve for \( y \)

Since \( (9y + 4)^{\circ} \) and \( (11y - 14)^{\circ} \) are vertical angles, we have \( 9y+4 = 11y - 14 \).
Subtract \( 9y \) from both sides: \( 4=2y - 14 \).
Add \( 14 \) to both sides: \( 18 = 2y \).
Divide both sides by \( 2 \): \( y = 9 \).

Step2: Solve for \( x \)

First, find the measure of the angle adjacent to \( (3x + 28)^{\circ} \).
The sum of angles around a point is \( 180^{\circ} \). The angle adjacent to \( (3x + 28)^{\circ} \) is \( 9y+4 \). Substitute \( y = 9 \), so \( 9\times9+4=81 + 4=85^{\circ} \).
Also, \( (3x + 28)+63+85=180 \) (sum of angles on a straight - line).
Simplify the left - hand side: \( 3x+28+148 = 180 \), then \( 3x+176 = 180 \).
Subtract \( 176 \) from both sides: \( 3x=4 \).
Divide both sides by \( 3 \): \( x=\frac{4}{3} \).

Answer:

\( x = \frac{4}{3}, y = 9 \)