Tangent Lines and Angle Relationships

This lesson covers the properties of tangent lines to a circle, including the definition of a tangent line and the point of tangency. It introduces the tangent perpendicular to radius theorem, which states that a tangent line is perpendicular to the radius at the point of tangency. The lesson then applies this theorem to solve a problem involving angles in a quadrilateral formed by tangent segments to a circle, demonstrating how to calculate unknown angle measures using the angle sum theorem.

What is a tangent to a circle?

• A line that intersects the circle at exactly one point

• A line that is inside the circle

• A line that is parallel to the circle

• A line that intersects the circle at two points

What is the point called where a tangent touches a circle?

• Radius

• Diameter

• Point of tangency

• Center

According to the Tangent Perpendicular to Radius Theorem, what is the relationship between a tangent and the radius at the point of tangency?

• They are equal

• They form an acute angle

• They are perpendicular

• They are parallel

If a line is tangent to a circle, what can be said about its angle with the radius at the point of tangency?

• It forms a 45-degree angle

• It forms a 90-degree angle

• It forms a 180-degree angle

• It forms a 60-degree angle

In the problem involving segments ML and MN, what shape is formed by the points L, M, N, and O?

• Triangle

• Quadrilateral

• Pentagon

• Hexagon

What is the sum of the interior angles of a quadrilateral?

• 450 degrees

• 180 degrees

• 270 degrees

• 360 degrees

Given angles L and N are 90 degrees, and angle O is 117 degrees, what is the measure of angle M?

• 63 degrees

• 90 degrees

• 117 degrees

• 180 degrees

How do you calculate the sum of angles in a polygon?

• Number of sides plus 2 times 180

• Number of sides minus 2 times 180

• Number of sides times 180

• Number of sides times 90