Question

Can a quadrilateral $GRAY$ with the following measures be constructed?
$\angle G={90}^o$, $\angle R={40}^o$, $\angle A={20}^o$, $\angle Y={180}^o$, GR= 8 cm and AR=5 cm.
If no, then find the correct reason.

• A. Sum of measures on interior angles of $\square GRAY$ is not ${360}^o$.
• B. Sum of measures on interior angles of $\square GRAY$ is not ${180}^o$.
• C. Length of one more side is required for construction
• D. None of the above

Answer 1

Answer: (A)

Sum of measures on interior angles of $\square GRAY$ is not ${360}^o$.

$\Rightarrow$ We have given quadrilateral $GRAY$,

$\Rightarrow$ $\angle G={90}^{\circ },\angle R={40}^{\circ },\angle A={20}^{\circ },\angle Y={180}^{\circ }$ {Given]

$\Rightarrow$ We know that sum of measures of all interior angles in quadrilateral is ${360}^{\circ }$.

$\Rightarrow$ By adding interior angles in quadrilateral $GRAY$ we get is ${330}^{\circ }$ which is not equal to ${360}^{\circ }$.

$\therefore$ $\square GRAYcannotbeconstructedbecausesumofmeasuresoninterioranglesisnot{360}^{\circ }$