Question

In a triangle ABC, the measure of angle B is 4 times the measure of angle A, and the measure of angle C is 17° less than 5 times the measure of angle A. Find the measure of the angles.​

Answer 1

A: 19.7º B: 78.8º C: 81.5º

Explanation:

The trouble with problems like this is usually just getting started.

Hint: look at the descriptions of the angle measures and see if one of the angles is mentioned twice. It's angle A. Pick a variable for the measure of that angle, say a.

Angle B: "4 times the measure of angle A" becomes 4a

Angle C: "17 less than 5 times the measure of angle A" becomes 5a - 17

Now use the fact that relates all three angles: the sum of the measures of any triangle's angles is 180 degrees.

a + 4a + (5a - 17) = 180

Combine like terms.

10a - 17 = 180

Add 17.

10a = 197

Divide by 10.

a = 19.7 degrees

Try not to panic because the answer is not a whole number!

Plug this into the expressions for the other angles.

B: 4(19.7) = 78.8 degrees

C: 5(19.7) - 17 = 81.5 degrees

Check: 19.7 + 78.8 + 81.5 = 180