Find the measure of each marked angle.

Question

Accepted Answer

Welcome back. I am so glad you're here. We're told in the following figure, solve for the value of the indicated angles in degree measure. We have a figure we are told that P and Q are parallel lines and then the intersecting line has two angles labeled, they are alternate exterior angles and one is labeled five X plus 10 degrees and the other is labeled nine X minus degrees. Our answer choices are answer choice. A 60 degrees, 120 degrees. Answer choice B 30 degrees, 30 degrees. Answer choice C 60 degrees, 60 degrees and answer choice D 10 degrees, 10 degrees. All right. Essentially, we need to solve for these two angles, the five X plus 10 degrees and the nine X minus 30 degrees. But because P and Q are parallel lines and because these two are alternate exterior angles, they are congruent. So that means they're equal to each other and setting them equal to each other. That means we can solve for X, we can set aside the parentheses and the degrees for a moment so that we can just solve this for X, we can take from the left hand side, we can subtract five X and si subtract five X from the other side as well. And then we can add 30 from the right hand side and add that to both sides. So on the left, five X minus five X is 0, 10 plus 30 is 40. So we have 40 on the left equals on the right nine X minus five X is four X and negative 30 plus 30 is zero. So we have 40 equals four, X dividing both sides by four, we will get an X value equal to 40 divided by four is 10. But remember that's not our degrees. That's just X. So now we have to go back and plug X in to solve for our angle measures. We have five multiplied instead of by X, we'll plug in 10 plus 10, 5 multiplied by 10 is 50. So 50 plus 10, that equals 60 we have 60 degrees here and because they are equal to each other, they're both going to be 60 degrees. So they're both equals to 60 degrees. We look at our answer choices and that matches with answer choice. See, well done. We'll catch you on the next one.

Find the measure of each marked angle.

Key Concepts

Angle Measurement

Properties of Angles

Trigonometric Ratios

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