Exploring Circle Theorems and Inscribed Angles

What is the measure of an angle formed inside a semicircle?

• 360 degrees

• 45 degrees

• 90 degrees

• 180 degrees

What does a diameter of a circle divide it into?

• Two equal halves

• Three equal parts

• Unequal segments

• Four equal quarters

If an angle in a semicircle is represented by the equation 11x + 2 = 90, what is the value of x?

• 8

• 10

• 11

• 12

What is the result of subtracting 2 from both sides of the equation 11x + 2 = 90?

• x = 88

• 11x = 88

• 11x = 92

• x = 8

What is the next step after simplifying the equation 11x = 88?

• Add 11 to both sides

• Subtract 11 from both sides

• Divide both sides by 11

• Multiply both sides by 11

What theorem states that angles intercepting the same arc are equal?

• Central Angle Theorem

• Inscribed Angle Theorem

• Corollary to the Intercepted Arc

• Alternate Segment Theorem

What theorem is applied when more than one chord intercepts the same arc?

• Corollary to the Intercepted Arc

• Chord Length Theorem

• Tangent Secant Theorem

• Secant Tangent Theorem

If angle B is 2x and angle C is x + 10, and they intercept the same arc, what is the value of x?

• 20

• 15

• 10

• 5

What is the value of angle B if x is found to be 10?

• 10 degrees

• 15 degrees

• 20 degrees

• 25 degrees

What is the value of angle C if x is found to be 10?

• 40 degrees

• 30 degrees

• 20 degrees

• 10 degrees