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

Hello, everyone. We are asked to find the measure of the indicated angles. Our angles are angle A which has a measure of the parentheses nine X minus 118 closed parentheses degrees or angle B which has a measure of in parentheses five X minus 46 degrees. Our answer choices are A, A equals 88 degrees. B equals 88 degrees B A equals 88 degrees. B equals 44 degrees C A equals 44 degrees. B equals 88 degrees D A equals 44 degrees B equals 44 degrees. So first looking at the orientation of angle A and angle B, I noticed they share a vertex and because of this, they are considered to be vertical angles. And I also know that vertical angles are congruent. So this means we can set the measure of A nine X minus 118 equal to the measure of B five X minus 46 and solve for X. So I'm gonna start to sulfur X by subtracting five X from both sides. So we have four X minus 118 equals negative 46. Then I'm gonna add 118 to both sides. So we have four, X equals to find the value of X, I divide both sides by four and X equals 18. This isn't our final answer, but this is a good step along the way. So I need to find the measure of the actual angle. Knowing that they're congruent means I can plug X into either A or B, it won't change what I do. I'm gonna go with B so B again equals parentheses, five, X minus 46 parent, close parentheses degrees. So we're gonna have five multiplied by 18, minus 46 degrees. Five multiplied by 18 is minus 46 degrees. So this comes out to 44 degrees. So we know that B equals 44 degrees. Since their vertical angles and vertical angles are congruent, we also can say that A equals 44 degrees. We don't have to plug it all the way back in. So this is answer choice D A equals 44 degrees. B equals 44 degrees. 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

Angle Measurement

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