Question

In the given figure, PQ || RS. Find the values of a, b and c.

• A. 20°, 40°, 120°
• B. 10°, 60°, 110°
• C. 30°, 50°, 100°
• D. 15°, 55°, 110°

Answer 1

The correct option is A 20°, 40°, 120°


Given, PQ || RS, and AC and BC are the transversals.
$\angle BCS=\angle PBC$
(Since alternate interior angles are equal)
$\Rightarrow b={40}^{\circ }$

Similarly, $\angle RCA=\angle BAC$
$\Rightarrow c={120}^{\circ }$

We know that sum of angles on a straight line is 180 degrees.
$\Rightarrow c+a+b=180°$
$\Rightarrow {120}^{\circ }+a+{40}^{\circ }={180}^{\circ }$
$\Rightarrow a={180}^{\circ }-{160}^{\circ }={20}^{\circ }$

Hence, ​​​​​​​$a={20}^{\circ },b={40}^{\circ }andc={120}^{\circ }$