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 solved for the value of the indicated angles in degree measure. We're given a figure with a triangle. The triangle's three angles are labeled one is three X plus three degrees. The second is four X degrees and the third is two X minus 12 degrees. Our answer choices are answer choice. A 66 degrees, 84 degrees, 30 degrees. Answer choice, B 72 degrees, 88 degrees, 20 degrees. Answer choice C 56 degrees, 84 degrees, 40 degrees and answer choice D 72 degrees, 78 degrees, 30 degrees. All right, we need to solve for the measurement for each of these angles. And we know that when you add all three angles of a triangle together, they equal 180 degrees. So we can add all these three up, set that equal to 180 degrees. Solve for X and then plug that back in which will give us each of our angles measurements. So I'm going to write these all without the parentheses and without the degrees. But we've got three X plus three for the first measurement and then we're adding, so plus the second one is four X, then plus adding the 3rd +12 X minus 12. These are all equal to 180 when they're added together. Now let's solve for X, combining like terms on the left hand side. Three X plus four, X plus two, X is nine X. And then we've got a plus three minus 12, which is a negative nine and that's still equal to 180. Now, we can add nine to both sides of the equal sign on the left. We just have nine X that equals on the right 189 dividing both sides by nine, we have X equals 189 divided by nine is a positive 21. So we've got X, now we can plug that in for each of the angle measurements and solve for the angles. So the first one, three X plus three degrees substituting in for X our 21. So this gives us three multiplied by 21 plus three degrees. Three, multiplied by 21 is 63. So we have 63 plus three degrees and 63 plus three equals 66. So that first angle is degrees. Now, the next one, we've got four X degrees again, substituting in for that X at 21. So we have four multiplied by 21 degrees and four multiplied by 21 is 84 So that second angle is 84 degrees. Now, the third one, we've got two X minus degrees substituting in for the X. So we'll have two multiplied by, instead of X 21 minus degrees, two multiplied by 21 is 42. So 42 minus 12 degrees and 42 minus 12 is 30. So the final one is 30 degrees. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

Find the measure of each marked angle.

Key Concepts

Angle Relationships

Trigonometric Ratios

Geometric Properties of Triangles

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