Angles in Circles

Where an angle sits changes what it measures.

12 problems · about 21 minutes · G-C.A.2

NameDate

Figure — use these to answer the problems

Change the angle. At the centre it equals its arc; on the circle it would be half of it.

80°

Angle in degrees80

Figure 1

Straightforward practice. Get the method working first.

5 problems

An arc of 120°. What is the inscribed angle on it, in degrees?
Answer
2
What decides whether an angle equals its arc or halves it?
- Whether the vertex is at the centre or on the circle.
- The size of the arc.
An arc of 100°. Inscribed angle on it, in degrees?
Answer
An arc of 100°. Central angle on it, in degrees?
Answer
An inscribed angle of 35°. What is its arc, in degrees?
Answer

The same ideas with more to keep track of.

3 problems

The angle between a tangent and the radius at the point of contact, in degrees?
Answer
One tangent from a point is 12 long. How long is the other?
Answer
How many points does a tangent share with the circle?
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

9
Match each angle type with its relationship to its arc.
Draw a line from each item on the left to its match on the right.
- Central angle
- Inscribed angle
- Angle in a semicircle
- Equal to the arc
- Half the arc
- Always 90 degrees
An arc of 140°. Inscribed angle, in degrees?
Answer
The Inscribed Angle
An arc measures 80°. What is the inscribed angle on it, in degrees?
Answerdegrees
The Semicircle
An angle inscribed in a semicircle. What is its measure, in degrees?
Answerdegrees