The angles in the same segment are equal | Maths | Quizalize & Oak National Academy

Starter quiz

An angle at the circumference of a circle is subtended by the diameter of that circle. What is the size of this angle (in degrees)?

30°

45°

60°

90° ✓

Not enough information.
The size of the angle labelled $x$ ° is ______°.

'162' ✓
The size of the angle labelled $y$ ° is ______°.

'81' ✓
The size of the angle labelled $z$ ° is ______°.

'81' ✓
The image shows a circle with centre O. A triangle is formed from two radii and a chord. A tangent to the circle is shown. The size of the angle labelled $a$ ° is ______°.

'31' ✓
Find the size of angle $b$ ° (in degrees).

'59' ✓

Find the size of angle $x$ ° on this 18-point geoboard.

4°

18°

20°

80° ✓

90°
Find the size of angle $y$ ° on this 18-point geoboard (in degrees).

'40' ✓
The image shows an 18 point geoboard. The size of the angle labelled $z$ ° is ______°.

'40' ✓
Both ∠ACB and ∠ADB are angles at the circumference subtended by the chord AB. The size of the angle labelled $k$ ° is ______°.

'31' ✓
Both ∠GHF and ∠GIF are angles at the circumference subtended by the chord GF. The size of the angle labelled $p$ ° is ______°.

'38' ✓
Both ∠JMK and ∠JLK are angles at the circumference subtended by the arc JK. The size of the angle labelled $t$ ° is ______°.

'71' ✓

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A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments
Theorems can be thought of as puzzles to solve, you are showing how to find a result
In order to use this theorem, you may need to draw a diagram or add more information to an existing one

Pupils may reason that two angles are the same size, as they are subtended by the same chord.

Angles are equal, if they are in the same segment, subtended by the same arc, as well as subtended by the same chord.

Theorem - A theorem is a statement that can be proved using known mathematical facts and reasoning.
Subtended - An angle can be subtended by a line segment or curve. The legs of the subtended angle meet the endpoints of the line segment or curve.
Chord - A chord is any line segment joining two points on the circumference of a circle.
Segment - Two segments are created when dividing a circle into two parts using a chord.