Question

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°.)

Answer 1

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

Explanation:

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

`\beta = 45 + 3\theta` (1)

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

`\beta + \theta + \theta = 180 ^(\circ)` (2)

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

`45 + 3\theta + \theta + \theta = 180`

`5\theta = 180 - 45`

`\theta = 27`

Hence, the third angle is:

`\beta = 45 + 3\theta = 45 + 3*27 = 126`

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

I hope it helps you!