Question

If 5∠A = 3∠B = ∠C, ∠A and ∠B are complementary angles, then the measure of ∠A, ∠B and ∠C are respectively VALUE OF A,B AND C 280°, 57°, 160°(a) 33.75°, 56.25°, 168.75°(B) 281°, 56°, 168°(C) 271.50°, 58.25°, 160.75°(D)

Answer 1

Given :  5∠A = 3∠B = ∠C, ∠A and ∠B are complementary angles

To Find : measure of ∠A, ∠B and ∠C

Solution:

5∠A = 3∠B = ∠C

∠A and ∠B are complementary angles,

complementary angles,  which adds up to 90° ( Right angle )

∠A + ∠B = 90°

=> 3∠A + 3∠B = 270°

=> 3∠A + 5∠A = 270°

=> 8∠A = 270°

=> ∠A = 270°/8

=> ∠A =  135°/4

=> ∠A  = 33.75°

∠A + ∠B = 90°

=> 33.75°+ ∠B = 90°

=> ∠B =  56.25°

∠C = 5∠A  = 5 * 33.75°

=> ∠C = 168.75°

A = 33.75°, B = 56.25°, C = 168.75°

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