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Mathematics · Self Assessment

Practice Test: Angle Properties, Polygons & Circle Theorems

A 100-mark paper covering "Geometry: Angles, Polygons & Their Properties" and "Circle Theorems" — multiple choice, true/false, fill-in-the-blank, column matching, and short answer, all auto-graded instantly.

EDUSAMBAM Editorial Team · 45 questions · 100 marks · Instant self-assessment

Questions

100

Marks

Sections

100%

Auto-Graded

Section	Questions	Marks Each	Total
A — Multiple Choice	15	2	30
B — True / False	10	2	20
C — Fill in the Blank	10	2	20
D — Column Matching	5 pairs	2	10
E — Short Answer	5	4	20
Total	45	—	100

Fill-in-the-blank and short-answer questions are checked automatically against accepted answers — exact wording doesn't need to match, but the key term should be present.

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Section A — Multiple Choice

30 marks

15 questions · 2 marks each.

1.Angles on a straight line always sum to:Basic2 pts

A. 90°

B. 360°

C. 180°

D. 270°

2.Where two straight lines cross, vertically opposite angles are always:Basic2 pts

A. Equal

B. Supplementary

C. Complementary

D. Always 90°

3.A transversal crosses two parallel lines. The alternate angles formed are:Intermediate2 pts

A. Supplementary

B. Always 90°

C. Unrelated

D. Equal

4.A triangle's two interior opposite angles are 50° and 65°. Its exterior angle at the third vertex is:Intermediate2 pts

A. 65°

B. 115°

C. 180°

D. 50°

5.The interior angle sum of a hexagon (6 sides) is:Intermediate2 pts

A. 540°

B. 900°

C. 360°

D. 720°

6.The exterior angles of any convex polygon always sum to:Intermediate2 pts

A. 180°

B. 360°

C. (n − 2) × 180°

D. It depends on the number of sides

7.A regular polygon has an exterior angle of 45°. How many sides does it have?Advanced2 pts

A. 8

B. 6

C. 9

D. 5

8.AB is a diameter of a circle, and C is a point on the circumference. Angle ACB equals:Basic2 pts

A. 45°

B. 180°

C. 90°

D. 60°

9.The angle at the centre of a circle, compared to the angle at the circumference on the same arc, is:Intermediate2 pts

A. Half as large

B. Twice as large

C. Equal

D. Three times as large

10.Angles in the same segment, subtending the same arc, are:Intermediate2 pts

A. Supplementary

B. Complementary

C. Unrelated

D. Equal

11.In a cyclic quadrilateral, opposite angles always:Intermediate2 pts

A. Are equal

B. Sum to 360°

C. Sum to 180°

D. Sum to 90°

12.A tangent meets the radius drawn to the point of contact at:Basic2 pts

A. 90°

B. 45°

C. 60°

D. It varies

13.Two tangents drawn from the same external point to a circle are:Intermediate2 pts

A. Equal in length

B. Parallel

C. Perpendicular to each other

D. Never equal

14.The alternate segment theorem relates the tangent-chord angle to:Advanced2 pts

A. The angle at the centre

B. The radius length

C. The angle in the alternate segment

D. The diameter

15.The region between a chord and an arc is called a:Basic2 pts

A. Sector

B. Segment

C. Tangent

D. Radius

Section B — True / False

20 marks

10 questions · 2 marks each.

16.Angles around a single point always sum to 360°.Basic2 pts

True

False

17.In an isosceles triangle, the two base angles opposite the equal sides are equal.Intermediate2 pts

True

False

18.A quadrilateral's interior angles always sum to 180°.Basic2 pts

True

False

19.Co-interior (allied) angles between two parallel lines sum to 180°.Intermediate2 pts

True

False

20.A regular polygon with n sides has n lines of symmetry.Intermediate2 pts

True

False

21.AB is a diameter of a circle. Any angle drawn from a point on the circumference to A and B is always 90°.Basic2 pts

True

False

22.The angle at the centre of a circle is always half the angle at the circumference on the same arc.Intermediate2 pts

True

False

23.In a cyclic quadrilateral, opposite angles are always equal to each other.Intermediate2 pts

True

False

24.A tangent to a circle touches it at exactly one point.Basic2 pts

True

False

25.The alternate segment theorem applies at the exact point where the tangent touches the circle.Advanced2 pts

True

False

Section C — Fill in the Blank

20 marks

10 questions · 2 marks each. Type the missing word or term.

26.Angles on a straight line always sum to ______ degrees.Basic2 pts

27.When two lines cross, the equal angles directly opposite each other are called ______ angles.Intermediate2 pts

28.The interior angle sum of a polygon with n sides is (n − 2) × ______.Intermediate2 pts

29.A polygon with all sides and all angles equal is called a ______ polygon.Basic2 pts

30.The exterior angles of any convex polygon always sum to ______ degrees.Intermediate2 pts

31.The longest chord of a circle, passing through the centre, is called the ______.Basic2 pts

32.An angle formed in a semicircle using the diameter is always a ______ angle.Basic2 pts

33.A quadrilateral with all four vertices on a circle is called a ______ quadrilateral.Intermediate2 pts

34.A tangent meets the radius drawn to the point of contact at ______ degrees.Intermediate2 pts

35.Two tangents drawn from the same external point to a circle are always ______ in length.Intermediate2 pts

Section D — Column Matching

10 marks

Match each term to its correct definition. Use the ▲▼ buttons to reorder Column B.

36–40.Match each term to its correct definition.Advanced10 pts

Column A

Exterior angle theorem

Cyclic quadrilateral

Tangent

Regular polygon

Alternate segment theorem

Column B

A straight line that touches a circle at exactly one point

Equals the sum of the two interior opposite angles

The tangent-chord angle equals the angle in the alternate segment

A four-sided shape with every vertex on a circle

A polygon with all sides and all angles equal

Section E — Short Answer

20 marks

5 questions · 4 marks each. Answer in one or two sentences.

41.Explain why the exterior angle of a triangle equals the sum of the two interior opposite angles.Advanced4 pts

42.Describe how to find the number of sides of a regular polygon if you know its exterior angle.Advanced4 pts

43.Explain what makes a triangle isosceles, and how this affects its angles.Intermediate4 pts

44.Describe the relationship between the angle at the centre and the angle at the circumference of a circle, for the same arc.Advanced4 pts

45.Explain why the angle in a semicircle is always 90°.Advanced4 pts

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