The measure of ∠A in △ABC is twice the measure of ∠B , and the measure of ∠C is 20° less than the measure of ∠B . What are the measures of the angles in △ABC ?

Answer 1

A = 2B

C = B-20

A +B +C = 180 for any triangle sum of all 3 angles always = 180 degrees

3 equations 3 unknowns

solve by substitution elimination, eliminate A and C by substituting equivalent expression in terms of B

A + B + C = 180 replace A with 2B, replace C with B-20

2B + B + B-20 = 180 combine like terms

4B = 200 divide both sides by 4

B = 200/4 = 50 degrees = angle B

A = 2B = 100 degrees = angle A

C = B-20 = 30 degrees = angle C

100 + 50 + 30 = 180