P, Q and R are the three angles of a triangle. If P − Q = 20° and Q − R = 26°, then ∠P is equal to:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 82°.
P, Q, and R are the three angles of the triangle.
P - Q = 20°
⇒ Q = P - 20°
Also, Q - R = 26°
⇒ R = Q - 26°
⇒ R = P - 20° - 26° = P - 46°
The sum of three angles of a triangle = 180°
P + Q + R = 180°
⇒ P + (P - 20°) + (P - 46°) = 180°
⇒ 3P = 246°
⇒ P = 246°/3 = 82°
Therefore, ∠P is equal to 82°.