Question

(a) In the given figure, prove that lines lm & nq are parallel to each other.

(b) What is the value of "x” if AB is parallel to CD in the figure?

[3 MARKS]

Answer 1

(a) Steps: 1 Mark
Proof: 1 Mark
(b) Solution: 1 Mark

(a) Given, $\angle lst={105}^{\circ }$ and $\angle nts={75}^{\circ }$

$\angle lst+\angle nts={105}^{\circ }+{75}^{\circ }={180}^{\circ }$

But these are co-interior angles.

Since co-interior angles are supplementary, lines are parallel.

Hence, the lines lm and nq are parallel.


(b) Since AB is parallel to CD, corresponding angles will be equal.

Therefore, x = 130°