Circle theorem proofs practice questions with answers

Answer: 40 degrees, the edge angle is half the centre angle on the same arc

1. Half of 80.
2. Say that the edge is half the centre.

• Method (1): Half of 80.
• Accuracy (1): Answer 40 degrees, the edge angle is half the centre angle on the same arc

Answer: 70 degrees, the edge angle is half the centre angle on the same arc

1. Half of 140.
2. Include the half-angle reason.

• Method (1): Half of 140.
• Accuracy (1): Answer 70 degrees, the edge angle is half the centre angle on the same arc

Answer: 56 degrees, the centre angle is twice the angle at the edge on the same arc

1. Double 28.
2. Name the same-arc theorem as the reason.

• Method (1): Double 28.
• Accuracy (1): Answer 56 degrees, the centre angle is twice the angle at the edge on the same arc

Answer: 45 degrees, the edge angle is half the centre angle on the same arc

1. Half of 90.
2. Name the theorem.

• Method (1): Half of 90.
• Accuracy (1): Answer 45 degrees, the edge angle is half the centre angle on the same arc

Answer: 70 degrees, the centre angle is twice the angle at the edge on the same arc

1. They went the wrong way along the theorem.
2. The centre is 70, with the double reason.

• Method (1): They went the wrong way along the theorem.
• Accuracy (1): Answer 70 degrees, the centre angle is twice the angle at the edge on the same arc

Answer: 25 degrees, the edge angle is half the centre angle on the same arc

1. Half of 50 is 25.
2. Use the edge wording.

• Method (1): Half of 50 is 25.
• Accuracy (1): Answer 25 degrees, the edge angle is half the centre angle on the same arc

Answer: 30 degrees each, because the radii are equal

1. 180 minus 120 equals 60, shared equally.
2. Each base angle is 30.

• Method (1): 180 minus 120 equals 60, shared equally.
• Accuracy (1): Answer 30 degrees each, because the radii are equal

Answer: 64 degrees, the centre angle is twice the angle at the edge on the same arc

1. Double 32.
2. The reason is the same-arc theorem.
3. 64 degrees with that reason.

• Method (1): Doubles 32 because both angles stand on the same arc
• Accuracy (1): 64 degrees with the reason

They must be on the same arc. The centre angle is twice the edge angle. They must be on the same arc. The centre angle is twice the edge angle.

60 degrees. 60 degrees.

50 degrees. 50 degrees.

Both radii are the same length, so the base angles are equal. Both radii are the same length, so the base angles are equal.

50 degrees each. The leftover 100 degrees is shared. 50 degrees each. The leftover 100 degrees is shared.

The reason: same arc, or equal radii. The reason: same arc, or equal radii.

It does not say why halving is allowed. The same-arc theorem is the reason. It does not say why halving is allowed. The same-arc theorem is the reason.

No. The theorem does not apply to a different arc. No. The theorem does not apply to a different arc.

180 degrees, like any triangle. 180 degrees, like any triangle.

One comes from equal sides. The other comes from the same arc. One comes from equal sides. The other comes from the same arc.

44 degrees. 44 degrees.

70 degrees. 70 degrees.

Without the same arc, doubling is not justified. Without the same arc, doubling is not justified.

60 degrees. The triangle is equilateral. 60 degrees. The triangle is equilateral.

The radii are equal, so the triangle is isosceles. The radii are equal, so the triangle is isosceles.