Find the measure of each marked angle. See Example 2.

Question

Accepted Answer

Welcome back. Everyone in this problem, we want to determine the degree measure of the indicated angles for our answer choices. A is 57 degrees and 123 degrees. B is 75 and 105 degrees. C is 36 and 144 degrees and D is 63 and 117 degrees. Now, what are we trying to figure out here? We want the degree measure of the indicated angles which are specified on the diagram. And if we notice on the diagram, our angles are expressions negative seven X degrees and negative 13 X degrees. However, notice that both of these angles are on a straight line and we know recall that on a straight line, let's say we had two angles on a straight line angle, X and angle Y then angles on a straight line sum to 180 degrees. So if we can use that idea here, we'll be able to solve for the value of X and thus figure out what each angle would be. Now, let's see if we can do that. So since both angles sum to 180 that means negative seven X degrees plus negative 13 X degrees equals 180 degrees. Negative seven X plus negative 13 X equals negative X. And to figure out the value of X, we can divide both sides by negative 20 negative 20 divided by negative 20 equals one. So that would be X degrees and divided by negative 20 equals negative nine. Therefore X equals negative nine degrees. Now that we have the value of X, we will be able to figure out the value for each angle. So therefore, our angle for the expression negative seven X would actually be negative seven multiplied by negative nine which equals 63 degrees and negative X would be negative 13 multiplied by negative nine which equals 117 degrees. Therefore, our angles are 63 and 117 degrees which in our answer choices would have been answer choice. D Thanks a lot for watching everyone. I hope this video helped.

Find the measure of each marked angle. See Example 2.

Key Concepts

Angle Measurement Units

Properties of Angles

Use of Reference Angles and Trigonometric Ratios

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