Question

In triangle ABC the measure of angle B is thrice to the measure of angle C and the measure of angle A is half the sum of the measure of angle B and C find the measure of all angles and also state the type of triangle by cross multiplication method

Answer 1

Answer: A = 60° B = 90° C = 30°

1. B = 3(C) = 3C

2. A = 1/2 (B+C)

Substitute value of B = 3C

A = 1/2 (3C+C)

= 1/2 (4C)

= 2C

We know in a triangle sum of sides = 180°

So, A+B+C = 180°

Substitue value of B = 3C and A = 2C

2C + 3C + C = 180°

6C = 180°

C = 30°

So, A = 2×30° = 60°

B = 3×30° = 90°

C = 30°

Since, 1 angle (B) = 90°, the triangle is a right triangle.