Question

The following diagram shows parallel lines cut by a transversal. Which of the following statements is true?

• A. Complementary angle of $x$ is $\frac{x}{2}$
• B. Supplementary angle of $x$ is $2x$
• C. $x={30}^{\circ }$
• D. $x={120}^{\circ }$

Answer 1

Answer: (A), (B)

The correct options are
A

Complementary angle of $x$ is $\frac{x}{2}$

B

Supplementary angle of $x$ is $2x$

In the above figure since the two lines are parallel and cut by a transversal, using the property of corresponding angles:

=> 2x - 60${}^{\circ }$ = x

=> x - 60${}^{\circ }$ = 0

=> x = 60${}^{\circ }$
Supplementary angle of ${60}^{\circ }=180-{60}^{\circ }={120}^{\circ }=2x$
Complementary angle of ${60}^{\circ }=90-{60}^{\circ }={30}^{\circ }=\frac{x}{2}$