Question

part a
find the value of the variables in the given figure.

part b
explain your reasoning.
use alternate interior angles to find x. then use supplementary angles to find y.

Explanation:

Step1: Use alternate - interior angles property

Since alternate - interior angles are equal, we set up the equation for \(x\): \(8x−10 = 7x\).

$$8x−7x=10$$

$$x = 10$$

Step2: Use supplementary - angles property

The angle \((7x)^{\circ}\) and \((6y + 20)^{\circ}\) are supplementary (linear - pair), so \(7x+(6y + 20)=180\). Substitute \(x = 10\) into the equation: \(7\times10+(6y + 20)=180\).

$$70+6y+20 = 180$$

$$6y+90 = 180$$

$$6y=180 - 90$$

$$6y = 90$$

$$y = 15$$

Answer:

\(x = 10\), \(y = 15\)