Question

the second angle in a triangle is two thirds of the first angle.the third angle is 36 less than twice the second angle. find the angles​

Answer 1

Answer:

72°, 48° and 60°

Explanation:

Trick:

Sum of all interior angles of a triangle = 180°

Let a, b, c be the angles such that

b = ⅔ of a = 2a/3

c = 36° less than 2b = 2b - 36 = 4a/3 - 36

angles are { a, 2a/3, 4a/3 } --- eqn (i)

Angle sum = a + b + c = 180°

.'. a + 2a/3 + 4a/3 - 36 = 180

=> 3a - 36 = 180 or a = 72°

From eqn (i), the angles are 72°, 48° and 60°

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