P, Q and R are the three angles of a triangle. If P − Q = 20° and Q − R = 26°, then ∠P is equal to:

Question

Accepted Answer

Given: P - Q = 20° and Q - R = 26°. We know the sum of angles in a triangle is 180°.

Step 1: Express P and Q in terms of R.
From Q - R = 26°, we get Q = R + 26°.
From P - Q = 20°, we get P = Q + 20° = R + 26° + 20° = R + 46°.

Step 2: Use the triangle angle sum property:
P + Q + R = 180°
(R + 46°) + (R + 26°) + R = 180°
3R + 72° = 180°
3R = 180° - 72° = 108°
R = 108° / 3 = 36°

Step 3: Calculate P:
P = R + 46° = 36° + 46° = 82°

Step 4: Verify options:
The calculated P is 82°, which corresponds to option 4.

Correction: The correct answer is 82°, option 4.

Rechecking the options and calculations:
- P = R + 46°
- R = 36°
- P = 82°

Therefore, the correct answer is 82°.

Answer

Answer

Answer