Question

In the figure(not drawn to scale), DAE, CBH and ACG are straight lines, DAE$||$CBH$||$FG and CA$=$CB. Find x and y respectively.

• A. ${70}^o,{35}^o$
• B. ${110}^o,{145}^o$
• C. ${110}^o,{35}^o$
• D. ${140}^o,{20}^o$

Answer 1

Answer: (B)

${110}^o,{145}^o$

Given that $DAE||CBH||FG$

$\angle x+{70}^{\circ }={180}^{\circ }$ ....Consecutive interior angles of parallel line

$\angle x={110}^{\circ }$

$\angle x=\angle ACB={110}^{\circ }$ ....Alternate interior angles of parallel lines

In a $\Delta ABC$, we have

$CA=CB$

$\Rightarrow \angle BAC=\angle CBA={\left(\frac{180-110}{2}\right)}^{\circ }$ ....Angle s opposite to equal sides are also equal

$\Rightarrow \angle BAC=\angle CBA={35}^{\circ }$

We know that $CBH$ is a straight line.

Thus $\angle y+\angle CBA={180}^{\circ }$

$\Rightarrow \angle y+{35}^{\circ }={180}^{\circ }$

$\Rightarrow \angle y={145}^{\circ }$