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. …

Question

asked Dec 4, 2021 73.3k views

1 Answer

CorPao · Answer 1 · 2021-12-08T19:12:20+0000

Answer:

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!