Question

If AB || CD and T is a transversal then the measurement of $\angle n$ is:

• A. $22{\frac{1}{2}}^{\circ }$
• B. ${45}^{\circ }$
• C. ${90}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

$\angle BPQ+\angle DQP={180}^{\circ })$ (Co interior angles)

$2l+2m={180}^{\circ }$

$l+m={90}^{\circ }$

From $△PRQ$ :

$2n=l+m$......... (Exterior angle of a triangle)

$n=\frac{l+m}{2}$

$=\frac{90}{2}={45}^{\circ }$.