Question

yLab and Mastering3.3.43Question HelpIn triangle ABC, the measure of angle Bis 15 more than three times the measure of angle A. The measure of angle C is 45° more than the measure of angle A Find the measure ofeach angleAngle Ameasures *

Answer 1

∠A = 24°

∠B = 87°

∠A = 24°

Explanation:

The sum of angles in a triangle is 180 degrees

let measure of angle A = ∠A

∠B = 15 more than three times the measure of angle A

∠B = 15 + 3∠A

∠C = 45° more than the measure of angle A

∠C = 45° + ∠A

∠A + ∠B + ∠C = 180° (sum of angles in a triangle)

∠A + 15 + 3∠A + 45° + ∠A = 180

collect like terms:

∠A + 3∠A + ∠A + 15 + 45 = 180

5∠A + 60 = 180

5∠A = 180 -60

5∠A = 120

∠A = 120/5

∠A = 24°

∠B = 15 + 3∠A = 15 + 3(24)

∠B = 87°

∠C = 45° + ∠A = 45° + 24°

∠C = 69°