The angles of a triangle are (x – 35) °, (x – 20) ° and (x + 40) °.
Find the three angles.

Question

The angles of a triangle are (x – 35) °, (x – 20) ° and (x + 40) °.Find the three angles.

Philoid · Accepted Answer

Theorem 1: The sum of three angles is 180°.

i.e. ∠A + ∠B + ∠C = 180°

⇒ (x – 35)° + (x – 20)° + (x + 40)° = 180°

⇒ x – 35 + x – 20 + x + 40 = 180

⇒ 3x – 55 + 40 = 180

⇒ 3x – 15 = 180

⇒ 3x = 180 + 15

⇒ 3x = 195

⇒

⇒ x = 15