Centre angles and semicircles

Mathematics · Geometry · ages 15-16

Name ______________________ Date ____________

The angle at the centre is 120 degrees. What is the angle at the circumference on the same chord?
Answer: ______________
The angle at the centre is 80 degrees. What is the angle at the circumference on the same chord?
- 40
- 80
- 160
- 20
The angle at the centre is 80 degrees. What is the angle at the edge on the same chord?
- 40 degrees
- 80 degrees
- 160 degrees
Tom says any angle drawn in a semicircle is a right angle. Is Tom right?
Circle one: True False
The angle at the circumference is 32 degrees. What is the angle at the centre on the same chord?
Answer: ______________
The reflex centre angle is 260 degrees. What angle does the minor arc make at the edge?
- 100 degrees
- 130 degrees
- 50 degrees
A triangle is drawn in a semicircle. One acute angle is 35 degrees. What is the third angle?
- 90
- 55
- 125
- 35
Maya says two angles on the same chord in the same segment are equal. Is Maya right?
Circle one: True False
An angle on a diameter is 90 degrees. Which theorem names this reason?
- Angle in a semicircle
- Alternate segment
- Angles in the same segment
The angle at the centre is 148 degrees. What is the angle at the circumference on the same chord?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

60 · 120 over 2 = 60.
40 · Half of 80 is 40. The 160 option doubles instead of halving.
40 degrees · Halve the centre angle: half of 80 is 40.
True · The diameter makes 180 at the centre, halved to 90 at the edge.
64 · Double: 32 times 2 = 64.
50 degrees · Minor angle 100, halved to 50.
55 · Angles total 180: 180 minus 90 minus 35 = 55. The 90 option names the right angle, not the missing one.
True · Both equal half of one shared centre angle.
Angle in a semicircle · The diameter case has its own name: angle in a semicircle.
74 · 148 over 2 = 74.