The sum of two angles measures up to 180° then these angles are known as supplementary angles. The measure of ∠PSR is 120°.
When the sum of two angles measures up to 180° then these angles are known as supplementary angles of each other.
for example, ∠x + ∠y = 180°, therefore, the ∠x and ∠y are the supplementary angles of each other.
As we can see in the image that the measure of ∠PSQ is 60°, therefore, the measure of the ∠PSV will also be 60°, as both the angles are vertically opposite angles equal.
Now, since VR is a chord that intersects at S. Therefore, the ∠PSV and ∠PSR are supplementary angles to each other. Thus, we can write,
[tex]\angle PSV +\angle PSR = 180^o\\\\60^o +\angle PSR = 180^o \\\\\angle PSR = 180^o - 60^o = 120^o[/tex]
Thus, the measure of ∠PSR is 120°.
Learn more about Supplementary Angles:
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