Find the measure of each marked angle.

Question

Accepted Answer

Welcome back. I am so glad you're here. We are told in the following figure, solve for the value of the indicated angles in degree measure. We're given a figure that has one large triangle that's been divided into two smaller triangles for the smaller triangle that's to the left within the larger triangle. It has angles of M degrees, 90 degrees and 45 degrees for the triangle that's within the large triangle. But to the right, that has labeled angles N degrees and degrees. And then a third one that we do not have to find, we only need to find M and N our answer choices are answer choice AM degrees equals 65 degrees and degrees equals 45 degrees. Answer choice BM degrees equals 45 degrees and degrees equals 65 degrees. Answer choice cm degrees equals 20 degrees and degrees equals 45 degrees. And answer choice DM degrees equals 45 degrees and degrees equals 20 degrees. All right. So let's start with angle M. We're going to take a look at that smaller triangle that contains angle M and we've got a 90 degrees and then a 45 degrees. Well, we recall from previous lessons that when you add up the angles of a triangle, it's going to equal 180 degrees. So an M degrees plus a 90 degrees plus a 45 degrees needs to equal 180 degrees. Adding like terms, 90 degrees plus 45 degrees is 135 degrees. So M degrees plus 135 degrees equals degrees. Now, subtracting 135 degrees from both sides. On the left, we just have M degrees and on the right, 180 degrees minus 135 degrees is degrees. So our M is equal to 45 degrees. Now, let's solve for N we'll take a look at the larger triangle that contains those two smaller ones. We know that, that one has a 90 degree angle. It has a 25 degree angle and then the third angle is M degrees plus N degrees. So again, those all add up to 180 degrees, we have M degrees plus N degrees plus 25 degrees plus 90 degrees equals 180 degrees. But keep in mind, we do know what M degrees is equal to. So we can substitute in there 45 degrees plus N degrees plus 25 degrees plus degrees. All equals 180 degrees, adding like terms 45 degrees plus 25 degrees plus 90 degrees. All adds up to 160 degrees still plus N degrees and equal to 180 degrees. Subtracting 160 degrees from both sides. And we get N degrees equals on the left and on the right, 180 degrees minus 160 degrees equals degrees. So our N degrees is 20 degrees. We look at our answer choices and this matches with answer choice. D well done. We'll catch you on the next one.

Find the measure of each marked angle.

Key Concepts

Angle Relationships

Trigonometric Ratios

The Pythagorean Theorem

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