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. We are given a triangle or angle A is in parentheses, X plus 12 degrees angle B is in parentheses, 16 X minus 22 degrees angle C in parentheses is X plus 10 degrees. Our answer choices are A, A equals 22 degrees. B equals 138 degrees. C equals 20 degrees. Answer choice B A equals 20 degrees. B equals 138 degrees. C equals 22 degrees. Answer choice C A equals 138 degrees. B equals 22 degrees. C equals 20 degrees D A equals 22 degrees. B equals 20 degrees. C equals 138 degrees. The first thing to recall is that the sum of the interior angles of a triangle is 100 degrees. So the sum of the interior angles of a triangle totals to 180 degrees. So this means I can add up all of the numbers I'm given for each angle and set it equal to 180. So we will have in parentheses X plus 12 plus in parentheses. 16 X minus 22 plus the parentheses X plus 10 equals 180. Since all the parentheses are added together, I can ignore the parentheses and combine my like terms. So starting with the X's, I have one X 16 X and one X which totals to XX combining the constants, I have 12, negative 22 and 10. So 12 plus negative 22 is negative 10, negative 10 plus 10 is zero. OK. That works out. So the constance canceled out. So we have 18, X equals 180 to get X by itself, we divide both sides by 18. So yeah, X equals 10. So each X is worth 10 degrees. So now we can substitute this back in and find out our angles. So for A, we were given that A is X plus 12 degrees. So if X is 10, A is 10 plus 12 degrees, which would be 22 degrees. For angle B we were told initially it is 16 X minus 22 degrees. So this would be 16 multiplied by 10 minus 22 degrees. 16 multiplied by 10 is 160 minus 22 degrees would give us degrees. And then C we were told is X plus degrees. So plugging in the 10, 10 plus 10 degrees would be degrees. So A is 22 degrees. B is 138 degrees. C is 20 degrees. Looking at my answer choices. That is answer choice a 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 Notation and Measurement

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