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Line RS is tangent to circle Q at point R.


What is the measure of ∠SQR ?

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Line RS is tangent to circle Q at point R What is the measure of SQR Enter your answer in the box class=

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royalranger
If the line RS is tangent to the circle, then it is at a 90 degree angle to the circle at the point of contact.

Now that we know 2 angles, we can find the 3rd:

180 - 90 - 32 = 58

Using the tangent and radius theorem, the measure of ∠SQR is 58°.

What is Circle Geometry??

From the question, we are to determine the measure of ∠SQR

In the given diagram, QR is a radius

By the tangent and radius theorem,

If a tangent and a radius meet at the point of tangency, then they are perpendicular to one another

∴ ∠QRS = 90°

∠SQR + ∠RSQ + ∠QRS = 180° (Sum of angles in a triangle)

∠SQR + 32° + 90° = 180°

∠SQR + 122° = 180°

∠SQR  = 180° -  122°

∠SQR  = 58°

Hence, the measure of ∠SQR is 58°.

Learn more on Circle geometry here: https://brainly.com/question/21872415

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