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 50 degrees and 20 degrees B is degrees and 30 degrees C is 61 degrees and 29 degrees and D is 59 degrees and degrees. Now, what do we know so far? Well, we're trying to figure out the degree measure of our angles. And the problem is that they are written as expressions with an unknown variable. So if we can figure out the value of our unknown variable X, then we can figure out the degree measure of both our indicated angles. Now, how can we figure that? Well notice that both of these angles form a degree angle or a right angle? So the sum of both of those expressions that is four X plus nine degrees plus two X plus six degrees equals 90 degrees. Now, we have an equation. So if we are able to solve for X, then we can figure out the value for each expression. Now first, let's combine our like terms. Notice that four X and two X are alike. So we can combine those four X plus two, X equals six, X. Likewise nine and six are constants and nine plus six equals 15. So if six X plus 15 equals 90 that means to get six X by itself, I can subtract 15 from both sides. No, 15 minus 15 leaves me with six X on the left hand side and 90 minus 15 leaves us with 75 on the right hand side to get X, we can divide both sides by six and six, X divided by six equals X while 75 divided by six equals 12.5 or 12.5. So since X is 12.5 no, we'll be able to solve for each of our indicated angles because that means first, our angle that was four, X plus nine degrees should actually be four multiplied by 12.5 plus nine degrees. Four multiplied by 12.5 is 50 50 plus nine equals 59 degrees. Next, our angle with the expression two X plus six should actually be two multiplied by 12.5 plus six. Two, multiplied by 12.5 is 25 and 25 plus six equals 31. Therefore, both our angles are 59 degrees and degrees. When we look on our answer choices, that 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 Relationships

Trigonometric Ratios

Geometric Properties of Triangles

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