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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.​

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Answer:

A: 19.7º  B: 78.8º  C: 81.5º

Step-by-step 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

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