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 $45^\circ$.
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 $45^\circ$.
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