Question

(a) In the given figure, prove that $LX\parallel MY\parallel NZ$. [3 MARKS]

(b) If $k={50}^{\circ }$, then find 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 $k={50}^{\circ }$,

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

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