Question

Given that l||m, what is the measure of angle r?

Solution

We can see that angle r and the 98° angle are alternate interior angles and therefore must be congruent. So the measure of angle r is 98°.

Question

Given that p || r, solve for x.

Solution

Since these angles are alternate interior angles, they must be congruent (in other words, equal to each other). So 2x+34=52. When I solve this equation, I find that x=9.

Question

In the following diagram, r || p || m and m∠4=117°. Name all the angles equal to 63°

Solution

If m∠4=117°, then m∠1=63° because ∠4 and ∠1 form a line together, which equals 180°. Therefore m∠2=63° because ∠2 and ∠1 are vertical angles (across from each other on an intersection) and therefore must be congruent. ∠2 and ∠8 are alternate interior angles, so they must be congruent. ∠6 and ∠8 are another pair of vertical angles that are congruent. And last but not least, ∠6 and ∠9 are another pair of alternate interior angles and, therefore, congruent. I cannot draw any conclusions about angles 10 through 18 because they are on a different transversal than the angle I was given. So angles 1, 2, 8, 6, and 9 are equal to 63°.

Question

In the figure below, l || m and x=50. What is z-y?

Solution

If x=50, then y=50 because they are alternate interior angles. Therefore, z is 130 because y and z form a line together, which is 180°. So z-y = 130 - 50 = 80.