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

Question

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

Accepted Answer

Hello, everyone. We are asked to find the measure of the indicated angles. We have two intersecting lines and we are told angle A equals in parentheses nine X minus 16 degrees and angle B equals in parentheses three X plus 68 degrees. Our answer choices are A, A equals 17 degrees B equals 17 degrees B A equals 137 degrees B equals 17 degrees C A equals 17 degrees B equals 137 degrees D A equals 137 degrees B equals 137 degrees. Looking at the orientation of the angles we are given, I noticed these are vertical angles meaning they share a vertex, but they're kind of on the opposite side of each other. The other thing we know about vertical angles is that they are congruent or equal if we need to set them equal. So we are gonna set A equal to B in order to solve for X. So we would have nine X minus 16 equals three X plus 86. Solving for X, I'm gonna subtract three X from both sides. So I have 36 X minus 16 equals 86 I'm gonna add 16 to both sides to try to isolate the X. So I have six, X equals 102. And then to get X by itself, I divide both sides by six and X would equal 17. So now that I know what X equals, I can plug it back into either A or B and find an angle measure. So I'm gonna plug it back into B we were told B equals three X plus 86 in parentheses degrees. So this would be three multiplied by 17 and then we're adding 86 to it. Three multiplied by 17 is 51 plus 86 in parenti's degrees and adding those together, I get 137 degrees. So I know B equals 137 degrees. Now, I could plug X into A also but recall what we said at the beginning, vertical angles are congruent. That means if angle B is 137 degrees, angle A is also 137 degrees. So our answer choice that has both A and B as 137 degrees is answer choice. D have a nice day.

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

Using Algebra to Solve for Angles

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