If the measure of the third angle of the triangle is 45 ° more than three time the measure of either of the other two angles, find the measure of each angle of the triangle. (Recall that the sum of the measures of the angles of a triangle is 180°.)

The first and second angles are 27° and the third angle is 126°.

Step-by-step explanation:

We have that the third angle (β) is 45° more than three times the measure of either of the other two angles (θ):

    (1)

Also, the sum of the measures of the 3 angles is 180°:

  (2)

By entering equation (1) into equation (2) we have:

Hence, the third angle is:

Therefore, the first and second angles are 27° and the third angle is 126°.

I hope it helps you!

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