PART is an isoceles trapezium. Find the value of y.

9

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Solution

The correct option is A 9

PART is an isoceles trapezium.
TP = RA (Given)
Then, $∠$ TPA = $∠$ RAP = 64°.
Given $∠$ ART = (4(3y + 2))° and $∠$ TPA = 64°.

From the figure, AP || RT and AR will be the transversal.

Thus, $∠$ TRA + $∠$ RAP = 180°.
$\Rightarrow$ (4(3y + 2))° + 64° = 180°
$\Rightarrow$ (4(3y + 2))° = 180° - 64° = 116°.
$\Rightarrow$ (3y + 2)° = $\frac{116 °}{4}$ = 29°
$\Rightarrow$ 3y = 29° - 2° = 27°.
$\Rightarrow$ y = $\frac{27 °}{3}$ = 9

Hence the value of y = 9.

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