Question

Assertion (A): The three angles of a triangle are in the ratio 1 : 2 : 3. Then, the triangle is right angled.

Reason (R): The measures of the three angles of the triangle 30°, 60° and 90°.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. If the angles are $$x$$, $$2x$$ and $$3x$$, then $$6x=180^{\circ}$$, so the angles are $$30^{\circ}$$, $$60^{\circ}$$ and $$90^{\circ}$$. The triangle is therefore right angled.

Step 2 – Reason: R is true. The angles in this ratio have measures $$30^{\circ}$$, $$60^{\circ}$$ and $$90^{\circ}$$.

Step 3 – Link: The reason identifies a $$90^{\circ}$$ angle, which directly explains why the triangle is right angled.