Question

(a) In the given figure, prove that $lx\parallel my\parallel nz$. [3 MARKS]

(b) If $k={50}^{\circ }$, then what is the value of $\angle PSY$?

Answer 1

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

(a) $\angle xpb=\angle msp=k$ (Alternate Angles are equal)

$\Rightarrow lx\parallel my...\left(i\right)$.

$\angle psm=\angle srn=k$ (Corresponding Angles)

$\Rightarrow my\parallel nz...\left(ii\right)$.

From (i) and (ii)

$lx\parallel myandmy\parallel nz$

$\Rightarrow lx\parallel my\parallel nz$.


(b) Given $k={50}^{\circ }$,

$\angle PSY={180}^{\circ }-k$

$={180}^{\circ }-{50}^{\circ }={130}^{\circ }$