Question

If triangle ABC, ANGLE C IS 30 DEGREE MORE THAN ANGLE A BUT ANGLE A IS 15 DEGREE LESS THAN ANGLE B, FIND ALL ANGLE

Answer 1

Answer:

∠A = 45°

∠B = 60°

∠C = 75°

Step-by-step explanation:

∠C = 30°+∠A

∠A = ∠B - 15°

In a triangle sum of all angles is 180°.

∴∠A + ∠B + ∠C = 180°------------------------------eqn.1

Substitute ∠A and ∠C values in eqn 1.

∠B - 15° + ∠B + 30°+∠A = 180°

∠B - 15° + ∠B + 30° + ∠B - 15° = 180° (Again substituting ∠A in the eqn.)

Combine all the like terms.

∠B + ∠B + ∠B -15°-15°+30° = 180°

3∠B -30°+30°= 180°

3∠B = 180°

∠B = 180° / 3 = 60°

∴∠B = 60°

Substitute ∠B in ∠A equation.

∠A =  ∠B - 15°

∠A = 60° - 15°

∠A = 45°

Now, substitute ∠A in ∠C equation.

∠C = 30°+∠A

∠C = 30° + 45°

∠C = 75°

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