Question

In the given figure, if $PTRA$ is an isoceles trapezium, then the value of $y$ is:

• A. $7$
• B. $8$
• C. $11$
• D. $9$

Answer 1

The correct option is D $9$


Given, $PTRA$ is an isoceles trapezium.
$TP=RA$ (Given)
Then, $\angle TPA=\angle RAP={64}^{\circ }$
($\because$ In an isosceles trapezium, angles on each parallel sides are equal)

Given $\angle ART=\left(4\right(3y+2){)}^{\circ }$ and $\angle TPA={64}^{\circ }$.
Now, TR||AP and RA is the travsversal.
Thus, $\angle TRA+\angle RAP={180}^{\circ }(\text{Interior angles on the same side of the transversal are supplementary)}$
$\Rightarrow \left(4\right(3y+2){)}^{\circ }+{64}^{\circ }={180}^{\circ }\Rightarrow (4(3y+2){)}^{\circ }={180}^{\circ }-{64}^{\circ }={116}^{\circ }\Rightarrow (3y+2{)}^{\circ }=\frac{{116}^{\circ }}{4}={29}^{\circ }\Rightarrow 3y={29}^{\circ }-2^{\circ }={27}^{\circ }\Rightarrow y=\frac{{27}^{\circ }}{3}=9$

Hence the value of $y$ is $9.$