is tangent to circle P at point Q. Circle P is shown. Line segment P Q is a radius. Line segment Q R is a tangent that intersects the circle at point Q. A line is drawn from point R to point P and goes through a point on the circle. Angle Q P R is 53 degrees. What is the measure of angle R? 37° 53° 90° 97°

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calculista calculista · Answer 1 · 2020-03-18T16:51:23+01:00

Answer:

[tex]m\angle R=37^o[/tex]

Step-by-step explanation:

we know that

If Line segment Q R is a tangent to circle P at point Q

then

Line segment QR is perpendicular to line segment PQ (radius) and PQR is a right triangle

so

[tex]m\angle QPR+m\angle R=90^o[/tex] ---> by complementary angles in a right triangle

substitute the given value

[tex]53^o+m\angle R=90^o[/tex]

[tex]m\angle R=90^o-53^o=37^o[/tex]

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bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 2 · 2022-01-11T06:38:00+01:00

The measure of the angle R is 37 degrees. Thus option A is correct option.

Given-

Given that the QR is the tangent of the circle P. Thus it is in right angle and angle Q is equal to the 90 degrees.

We know that the sum of all the angles in a triangle is equal to the 180 degrees. therefore using the sum rule of the triangle, we get,

[tex]\angle PQR +\angle QRP +\angle QPR=180[/tex]

Put the value of the angle Q and angle P in the above equation we get,

[tex]90 +\angle QRP +53=180[/tex]

Rewrite and solve the equation for angle R

[tex]\angle QRP=180-90-53[/tex]

[tex]\angle QRP=37[/tex]

Hence, the measure of the angle R is 37 degrees. Thus option A is correct option.

For more about the circle follow the link below-

https://brainly.com/question/11833983