Question

Calculate the value of x, y & z.

• A. ${65}^{\circ }$, ${140}^{\circ }$, ${40}^{\circ }$
• B. ${115}^{\circ }$, ${40}^{\circ }$, ${40}^{\circ }$
• C. ${115}^{\circ }$, ${140}^{\circ }$, ${40}^{\circ }$
• D. ${15}^{\circ }$, ${140}^{\circ }$, ${140}^{\circ }$

Answer 1

The correct option is C ${115}^{\circ }$, ${140}^{\circ }$, ${40}^{\circ }$

∠z = ${40}^{\circ }$ [vertically opposite angles]
∠y + ∠z = ${180}^{\circ }$ [Linear pair]
∠y + ${40}^{\circ }$ = ${180}^{\circ }$
∠y = ${180}^{\circ }$ - ${40}^{\circ }$
∠y = ${140}^{\circ }$

Then, ${40}^{\circ }$+ ∠x + ${25}^{\circ }$ = ${180}^{\circ }$ [angles on straight line]
${65}^{\circ }$ + ∠x = ${180}^{\circ }$
∠x = ${180}^{\circ }$ – ${65}^{\circ }$
$\therefore \angle x={115}^{\circ }$