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Question

In triangle ABC, the measure of the largest angle is 32 less than 3 times the smallest angle. The measure of the middle angle is 8 more than half the measure of the largest angle. What is the measure of the middle angle?

   , the measure of the largest angle is 32 less than 3 times the smallest angle. The measure of the middle angle is 8 more than half the measure of the largest angle. What is the measure of the middle angle?  , the measure of the largest angle is 32 less than 3 times the smallest angle. The measure of the middle angle is 8 more than half the measure of the largest angle. What is the measure of the middle angle?

   , the measure of the largest angle is 32 less than 3 times the smallest angle. The measure of the middle angle is 8 more than half the measure of the largest angle. What is the measure of the middle angle? , the measure of the largest angle is 32 less than 3 times the smallest angle. The measure of the middle angle is 8 more than half the measure of the largest angle. What is the measure of the middle angle?

Answer 1

Let "x" be the measure of the smallest angle.

Then the largest angle is "3x - 32" and the middle angle is "8 + 1/2(3x - 32)".

There are 180 degrees in a triangle so adding the three angles gives us 180:

(x) + (3x - 32) + (8 + 1/2(3x - 32)) = 180

x + 3x + (3/2)x - 32 + 8 - 16 = 180

2x/2 + 6x/2 + 3x/2 - 40 = 180

11x/2 = 220

11x = 220(2)

11x = 440

x = 40

So the smallest angle is 40°

The largest angle is 3•40 - 32 = 120 - 32 = 88°

The middle angle is 8 + 1/2(88) = 8 + 44 = 52°