Questions: Assignment 13: Using Angle Pairs to Solve Problems (Two Transversals) Tip: When dealing with multiple transversals, try to focus on one pair of angles formed by one transversal at a time, "blocking out" the other. Solve for the first pair, then move on to the other transversal and repeat the process, using your first solution. In each diagram below, lines I and m are parallel. Find the values of both x and y.

Assignment 13: Using Angle Pairs to Solve Problems (Two Transversals)
Tip: When dealing with multiple transversals, try to focus on one pair of angles formed by one transversal at a time, "blocking out" the other. Solve for the first pair, then move on to the other transversal and repeat the process, using your first solution.

In each diagram below, lines I and m are parallel. Find the values of both x and y.

Transcript text: Assignment 13: Using Angle Pairs to Solve Problems (Two Transversals) Tip: When dealing with multiple transversals, try to focus on one pair of angles formed by one transversal at a time, "blocking out" the other. Solve for the first pair, then move on to the other transversal and repeat the process, using your first solution. In each diagram below, lines $I$ and $m$ are parallel. Find the values of both x and y .

Solution

Solution Steps

Step 1: Find x using the first transversal

The angles (3x)° and (7x-23)° are consecutive interior angles, so they are supplementary. Thus, 3x + 7x - 23 = 180. Simplifying gives 10x - 23 = 180. Adding 23 to both sides gives 10x = 203. Dividing by 10 gives x = 20.3.

Step 2: Find y using the second transversal

The angles 49° and (11y - 1)° are corresponding angles, so they are congruent. Thus, 11y - 1 = 49. Adding 1 to both sides gives 11y = 50. Dividing both sides by 11 gives y = 50/11 or approximately 4.55.

Step 3: Find x using the second transversal.

The angles (3x - 4)° and (5x - 38)° are consecutive interior angles, so they are supplementary. Thus, (3x-4) + (5x-38) = 180. Combining like terms gives 8x - 42 = 180. Adding 42 to both sides gives 8x = 222. Dividing both sides by 8 gives x = 27.75

Step 4: Find y using the first transversal

The angle (7y-20)° is complementary to the right angle, so 7y - 20 = 90. Adding 20 to both sides gives 7y=110. Dividing by 7 gives y = 15.71, approximately.