Question

One angle of a linear pair is twice the other. What is the value of the smaller angle?

(A) $120^{\circ}$ (B) $50^{\circ}$ (C) $40^{\circ}$ (D) $60^{\circ}$.

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Answer

Question: One angle of a linear pair is twice the other. What is the value of the smaller angle?

(A) $120^{\circ}$
(B) $50^{\circ}$
(C) $40^{\circ}$
(D) $60^{\circ}$

:

The correct option is (D) $60^{\circ}$.

To find the smaller angle when one angle is twice the other in a linear pair:

  1. Definition: A linear pair consists of two adjacent angles that sum up to $180^{\circ}$.

  2. Let the smaller angle be $\angle ABD$. Hence, the larger angle, $\angle DBC$, is twice the smaller angle: $$\angle DBC = 2\angle ABD.$$

  3. According to the property of a linear pair: $$\angle ABD + \angle DBC = 180^{\circ}.$$

  4. Substituting the value of $\angle DBC$: $$\angle ABD + 2\angle ABD = 180^{\circ}.$$

  5. Simplify: $$3\angle ABD = 180^{\circ}.$$

  6. Solving for $\angle ABD$: $$\angle ABD = \frac{180^{\circ}}{3} = 60^{\circ}.$$

  7. Therefore, the larger angle is: $$\angle DBC = 2 \times 60^{\circ} = 120^{\circ}.$$

Thus, the value of the smaller angle is $\mathbf{60^{\circ}}$.


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