Solving Equations and Inscribed Angles

The video tutorial explains how to find the measure of an inscribed angle in a circle. It begins by describing the properties of inscribed angles and how their measures relate to the arcs they create. The tutorial then demonstrates substituting algebraic expressions to represent these measures and solving for the variable x. Finally, it calculates the angle measure using the solved value of x.

What is an inscribed angle?

• An angle that is not related to a circle.

• An angle whose vertex is at the center of the circle.

• An angle formed by two chords in a circle.

• An angle formed outside the circle.

How can you identify an inscribed angle?

• All points of the angle are inside the circle.

• The vertex of the angle is on the circle.

• The angle is formed by two radii.

• The angle is larger than 180 degrees.

What is the relationship between an inscribed angle and its arc?

• The angle is unrelated to the arc.

• The angle is twice the measure of the arc.

• The angle is equal to the measure of the arc.

• The angle is half the measure of the arc.

If the measure of an inscribed angle is 1/2 the measure of its arc, what is the measure of the arc if the angle is 30 degrees?

• 90 degrees

• 60 degrees

• 120 degrees

• 15 degrees

What expression represents the measure of angle n ml?

• 2x + 3

• x + 51

• 26x

• 51x + 3

What expression represents the measure of Arc Ln?

• 26x

• 3x + 51

• x + 26

• 51x + 3

What is the purpose of substituting algebraic expressions in this context?

• To determine the radius of the circle.

• To find the length of the circle.

• To represent the measures of the angle and arc.

• To calculate the diameter of the circle.

What is the first step in solving the equation for x?

• Divide both sides by 2.

• Multiply both sides by 2.

• Subtract 26x from both sides.

• Add 51x to both sides.

After multiplying both sides by 2, what is the resulting equation?

• 51x = 52x + 3

• 52x = 51x + 3

• 26x = 51x + 3

• 51x = 26x + 3

What is the value of x after solving the equation?

• 1

• 2

• 3

• 4