the sum of the measure of 3 angles

Question

The sum of the measures of the three angles in any triangle is 180 degrees. The measure of the smallest angle of a certain triangle is half the measure of the second angle. The measure of the largest angle is

95 degrees° more than 2 times the measure of the smallest. Find the measure of each angle.

Answer 1

Hi, Brittany!

Okay, so let's call these angles, A,B and C

A + B + C = 180 , as you stated in the question.

Let's call A the smallest and C the largest.

Therefore,

A = (1/2)B because the measure of the smallest is half the measure of the second.

Also, since the largest is 95 degrees more than 2 times the smallest, then:

C = 2A + 95

So, since A = (1/2)B, then B = 2A

Now we have all the angles in terms of A:

A = A

B = 2A

C = 2A + 95

So now we can substitute them into our original equation A + B + C = 180

A + 2A + 2A + 95 = 180

5A = 180 - 95 = 85

A = 17

Now, we can figure all the angles.

A = 17 degrees

B = 2(17) = 34 degrees

C = 2(17) + 95 = 129 degrees