Question
In a quadrilateral $PQRS, \angle\text{P}=50^\circ,\angle\text{Q}=50^\circ,\angle\text{R}=50^\circ,\text{Find}\angle\text{S}$. Is this quadrilateral convex or concave?
✓
Answer
Given, a quadrilateral $PQRS$, where
$\angle\text{P}=50^\circ,\angle\text{Q}=50^\circ,\angle\text{R}=60^\circ$
Now, by the angle sum property of a quadrilateral, we have
$\angle\text{P}+\angle\text{Q}+\angle\text{R}+\angle\text{S}=360^\circ$
$\Rightarrow50^\circ+50^\circ+60^\circ\angle\text{S}=360^\circ$
$\Rightarrow\angle\text{S}=360^\circ-160^\circ$
$\Rightarrow\angle\text{S}=200^\circ$
Since, one interior angle of the given quadrilateral is obtuse, therefore the quadrilateral is concave.
$\angle\text{P}=50^\circ,\angle\text{Q}=50^\circ,\angle\text{R}=60^\circ$
Now, by the angle sum property of a quadrilateral, we have
$\angle\text{P}+\angle\text{Q}+\angle\text{R}+\angle\text{S}=360^\circ$
$\Rightarrow50^\circ+50^\circ+60^\circ\angle\text{S}=360^\circ$
$\Rightarrow\angle\text{S}=360^\circ-160^\circ$
$\Rightarrow\angle\text{S}=200^\circ$
Since, one interior angle of the given quadrilateral is obtuse, therefore the quadrilateral is concave.
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