Geometry

Question Analysis

This question involves solving for the variables x and y given two parallel lines cut by a transversal, with angle measures expressed algebraically. The focus is on identifying the relationship between given angles and using it to set up an equation for x and y.

 

Key Concept Explanation:

When two parallel lines are cut by a transversal, same-side interior angles are on the same side of the transversal and inside the two lines. The key property is that same-side interior angles are supplementary (add up to 180°).

 

A linear pair of angles is formed when two lines intersect. The two angles in a linear pair are adjacent, share a common side, and their non-common sides form a straight line. Their sum is 180 degrees.

 

Step-by-Step Solution:

Solve for x:

In this problem, the angles (7x - 21)° and (9x +9)° are linear pair angles, so we can set their measures to be supplementary (add up to 180) and solve for x:

(7x - 21) + (9x +9) = 180

16x - 12 = 180

16x = 192

x = 12

 

Solve for y:

The ...