Is tangent to circle p at point q. what is the measure of angle r? 37° 53° 90° 97°

Is tangent to circle p at point q. what is the measure of angle r? 37° 53° 90° 97°: A tangent at Q is perpendicular to the radius, forming a 90° angle.

Understanding tangents and circles is a fundamental concept in geometry. When a line, like PQ, touches a circle (represented by point P) at exactly one point (point Q), we call it a tangent line. This special relationship between the line and the circle unlocks a unique property – the angle formed by the radius (line segment connecting the center of the circle, O, to the point of tangency, Q) and the tangent line (PQ) is always a right angle (90 degrees).

This fact empowers us to solve for the measure of angle R in the scenario you’ve presented.

Analyzing the Answer Choices

Let’s analyze the possible measures for angle R:

• 37° and 53°: These values are too small to be a right angle. Remember, a right angle is a specific measurement of 90 degrees.
• 97°: This value is too large to be a right angle. As mentioned earlier, a right angle cannot exceed 90 degrees.
• 90°: Bingo! This is the only option that aligns with the property of a tangent line – the angle formed by the radius and the tangent is always a right angle, measuring precisely 90 degrees.

The Answer

Therefore, based on the geometric principle of tangents and circles, the measure of angle R is conclusively 90 degrees.