Question

The measure of the largest angle of a triangle is 10° more than the sum of the measures of the other two angles and 10° less than 3 times the measure of the smallest angle. Find the measures of the three angles of a triangle. (Show all the work).

Answer 1

A = 95°; B = 50°; C = 35 °

Explanation:

Let the three angles be A, B, and C, with A being the largest and C the smallest angle.

We have three conditions:

(1) A + B + C = 180

(2) A = B + C + 10

(3) A - 3C = -10

Let’s rearrange the equations to have the same form:

(4) A + B + C = 180

(5) A – B – C = 10

(6) A – 3C = -10

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Add Equations (4) and 5).

2A = 190 Divide each side by 2

A = 95°

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Substitute the value of A into Equation (6).

95 – 3C = -10 Subtract 95 from each side

-3C = -105 Divide each side by -3

C = 35°

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Substitute the values for A and C into Equation (4).

95 + B + 35 = 180

B + 130 = 180 Subtract 130 from each side

B = 50°

A = 95°; B = 50°; C = 35 °

Check:

(1) 95 +50 + 35 = 180

180 = 180

(2) 95 = 50 + 35 + 10

95 = 95

(3) 95 – 3× 35 = -10

95 – 105 = -10

-10 = -10