Question

(a) Prove that when two lines intersect, the vertically opposite angles are equal. [3 MARKS]
(b) Find the value of X in the given figure:

Answer 1

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


(a)

We have to prove $\angle 1=\angle 3\&\angle 2=\angle 4$

$\angle 1+\angle 2={180}^{\circ }$ [Linear pair]

$\Rightarrow \angle 1={180}^{\circ }-\angle 2$

Again, $\angle 3+\angle 2={180}^{\circ }$ [Linear pair]

$\Rightarrow \angle 3={180}^{\circ }-\angle 2$

Hence, $\angle 1=\angle 3$

Similarly, we can also prove that $\angle 2=\angle 4$.


(b) As $\angle$AOB = $\angle$DOE (vertically opposite angles)
So, $\angle$X = 60${}^{\circ }$