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Assertion (A): A triangle can have at most one right angle. Reason (R): The sum of the three angles of a triangle is 180°. Choose the correct option.

Class 9Lines and AnglesGeometry — Lines and Angles
  • ABoth A and R are true, and R is the correct explanation of A.
  • BBoth A and R are true, but R is not the correct explanation of A.
  • CA is true but R is false.
  • DA is false but R is true.

Step-by-Step Solution

If a triangle had two right angles, those two alone would total 180°, leaving 0° for the third — impossible. This follows directly from the angle-sum being 180°, so R correctly explains A.
Answer: A) Both A and R are true, and R is the correct explanation of A.

Key idea: Angle sum property of a triangle (180°)

**Theorem**: The sum of the three interior angles of a triangle is 180°.

**Proof sketch** (via parallel lines):
Draw a triangle ABC. Through vertex A, draw a line ℓ parallel to BC.
- Angle (between ℓ and AB) = ∠ABC (alternate interior).
- Angle (between ℓ and AC) = ∠ACB (alternate interior).
- The three angles at A — ∠ABC, ∠BAC, ∠ACB — together make a straight line (180°).
- Therefore ∠ABC + ∠BAC + ∠ACB = 180°. ∎

This ONE fact powers most triangle problems.

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