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 on our diagram. For our answer choices, A is 40 degrees and 140 degrees B is 34 and 146 degrees C is 3150 degrees and D is 43 and 137 degrees. Now, if we're going to figure out the measure of the indicated angles, the problem is that our angles are written as expressions and we don't know the value of our unknown term. So we need to figure out that unknown value before we can write down the degree measure. While we don't know what the value is. We know that both of these angles are on a straight line. And recall that Angus on a straight line angles on a straight line, some to 180 degrees. So we know that the sum of both these angles equals 180 degrees. Let's see if that can help us to figure out the unknown value. So this tells us that three X plus seven degrees plus X plus 11 degrees equals 180 degrees. Let's go ahead and solve for X. Now to do that first, let's group our like terms. Notice that three X is like 15 X and three X plus 15 X equals 18, X. Likewise seven and 11 are like terms and seven plus equals 18. Therefore 18 X plus 18 equals 180 degrees. Subtracting 18 from both sides, 18 X plus 18 minus 18 just leaves us with 18 X and 180 minus equals 162. If 18 X equals 162 that means X equals 162 divided by 18, which equals nine. Therefore, the value of X is nine degrees. Now that we know the value of X, we should be able to solve for our angles. So therefore, that means our anger. That was written as the expression three X plus seven degrees is actually three multiplied by nine plus seven and three multiplied by nine is 27 27 plus seven equals 34. Likewise, our angle that was 15, X plus 11 should actually be 15, multiplied by nine plus 11. 15, multiplied by nine is 135 and plus 11 equals 146 degrees. Therefore, our unknown angles would have been 34 and degrees. When we look on our list of answer choices that would have been choice. B thanks a lot for watching everyone. I hope this video helped.

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

Key Concepts

Angle Relationships

Trigonometric Ratios

Geometric Properties of Triangles

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