Find the measure of each marked angle. In Exercises 19–22, m and ...

Question

Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .

Accepted Answer

Given that the lines P and Q are parallel, find the measure of the indicated angles. Where we notice here we have a pair of parallel lines, P and Q and another line bisecting the two lines. And we have four possible answers all angles A and B and degrees of varying measures. Let's go ahead and solve this. Now, we know by geometry that this follows the alternate exterior angle theorem which states that if we have two angles by a bi setting line of two parallel lines, the exterior angles are both equal to each other. In other words, angles A and B should be equal to each other. Let's go ahead and solve for X. We have three X plus 19 equals five X minus 61. We can solve for X by first moving over power 19 by subtracting and we can move over our five by also subtracting our five X. We get negative to X as equals two, negative 80 divided both sides by negative two to get X is equals to 40. Now we can find the measures of our angles angle A should be three X plus 19 where X is equals to 40. We have three multiplied by 40 plus 19 to get degrees. Now we know angle A is the same as angle B. So B will also be 139 degrees. We now have our final answer. Both measures are 1 39 degrees, which means the answer to our problem is answer D OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .

Key Concepts

Parallel Lines and Transversals

Angle Relationships

Angle Measurement

Watch next