Question
If PQRS is a square, then write the measure of $\angle\text{SRP.}$
✓
Answer
The square PQRS is given as:
Since PQRS is a square.
Therefore,
PS = SR
and $\angle\text{PSR}=90^\circ$
Now, in $\triangle\text{PSR},$ we have
PS = SR
That is, $\angle\text{1}=\angle\text{2}$ (Angles opposite to equal sides are equal)
By angle sum property of a triangle.
$\angle\text{PSR}+\angle\text{1}+\angle\text{2}=180^\circ$
$\angle\text{PSR}+2\angle\text{1}=180^\circ$
$90^\circ+2\angle\text{1}=180^\circ$ $(\angle\text{PSR}=90^\circ)$
$2\angle\text{1}=90^\circ$
$\angle1=45^\circ$
Hence, the measure of $\angle\text{SRP}$ is 45°.
Since PQRS is a square.
Therefore,
PS = SR
and $\angle\text{PSR}=90^\circ$
Now, in $\triangle\text{PSR},$ we have
PS = SR
That is, $\angle\text{1}=\angle\text{2}$ (Angles opposite to equal sides are equal)
By angle sum property of a triangle.
$\angle\text{PSR}+\angle\text{1}+\angle\text{2}=180^\circ$
$\angle\text{PSR}+2\angle\text{1}=180^\circ$
$90^\circ+2\angle\text{1}=180^\circ$ $(\angle\text{PSR}=90^\circ)$
$2\angle\text{1}=90^\circ$
$\angle1=45^\circ$
Hence, the measure of $\angle\text{SRP}$ is 45°.
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