math calculations

Question

In triangle​ ABC, the size of angle B is

4times the size of angle​ A, and the size of angle C is 18

degrees less than 5times the size of angle A.

Find the size of the angles.

Answer 1

A= 19.9°

B = 79.2°

C = 81°

For any Triangle, all the angles must sum to 180

So A° + B° + C° = 180°

A = A°

B = 4A°

C =( 5A -18)°

A° + 4A° + (5A -18)° = 180°

10A° - 18° = 180°

Add 18 to both sides of the equation

10A° = 180° + 18°

10A° = 198°

Divide both sides by 10

A = 19.8°

B = 4(19.8°) = 79.2°

C = 5(19.8°) - 18° = 99° - 18° = 81°

Checking

19.8° + 79.2° + 81° = 180°