Q. 64.4( 28 Votes )
The angles of a triangle are arranged in ascending order of their magnitude. If the difference between two consecutive angles is 10°, find the three angles.
Answer :
Given:
Let the angles are :
∠A = x, ∠B = x + 10, ∠ C = x + 20
As we know, using theorem (1), in any triangle, sum of the three interior angles is 180°.
So,
∠A + ∠B + ∠ C = 180°
⇒ x + x + 10 + x + 20 = 180°
⇒ 3x + 30° = 180°
⇒ 3x = 180° - 30°
⇒ 3x = 150°
⇒ x = 50°
So, the angles are,
∠A = x = 50°
∠B = x + 10 = 50° + 10° = 60°
∠ C = x + 20 = 50° + 20° = 70°
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