Question

given m || n, find the value of x and y. (5x - 16)° (3x + 17)° (2y + 14)° answer attempt 1 out of 2 x = y =

Explanation:

Step1: Solve for \( x \) using alternate exterior angles

Since \( m \parallel n \), the angles \( (5x - 16)^\circ \) and \( (3x + 17)^\circ \) are alternate exterior angles, so they are equal.
\[
5x - 16 = 3x + 17
\]
Subtract \( 3x \) from both sides:
\[
2x - 16 = 17
\]
Add 16 to both sides:
\[
2x = 33
\]
Divide by 2:
\[
x = \frac{33}{2} = 16.5
\]

Step2: Solve for \( y \) using supplementary angles

The angle \( (3x + 17)^\circ \) and \( (2y + 14)^\circ \) are supplementary (they form a linear pair), so their sum is \( 180^\circ \). First, find \( 3x + 17 \) with \( x = 16.5 \):
\[
3(16.5) + 17 = 49.5 + 17 = 66.5
\]
Now set up the equation for supplementary angles:
\[
66.5 + (2y + 14) = 180
\]
Simplify:
\[
2y + 80.5 = 180
\]
Subtract 80.5:
\[
2y = 99.5
\]
Divide by 2:
\[
y = \frac{99.5}{2} = 49.75
\]

Answer:

\( x = 16.5 \), \( y = 49.75 \)