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Angles in Cyclic Quadrilaterals

In this worksheet, students must find missing angles in inscribed quadrilaterals.

'Angles in Cyclic Quadrilaterals' worksheet

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Curriculum subtopic:  Identify and Apply Circle Definitions and Properties

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

Opposite angles in a cyclic quadrilateral add up to 180°.

 

Example

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

 


 

Answer

+ 51° = 180°

= 180° - 51° = 129°

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

  • Question 1

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

CORRECT ANSWER
117
EDDIE SAYS
a° = 180° - 63°
  • Question 2

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

CORRECT ANSWER
69
EDDIE SAYS
a° = 180° - 111°
  • Question 3

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

CORRECT ANSWER
81
EDDIE SAYS
a° = 180° - 99°
  • Question 4

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

CORRECT ANSWER
85
EDDIE SAYS
a° = 180° - 95°
  • Question 5

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

CORRECT ANSWER
65
EDDIE SAYS
a° = 180° - 115°
  • Question 6

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

CORRECT ANSWER
57
EDDIE SAYS
a° = 180° - 123°
  • Question 7

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

CORRECT ANSWER
93
EDDIE SAYS
a° = 180° - 87°
  • Question 8

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

CORRECT ANSWER
109
EDDIE SAYS
a° = 180° - 71°
  • Question 9

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

CORRECT ANSWER
48
EDDIE SAYS
a° = 180° - 132°
  • Question 10

ABCD is a cyclic quadrilateral, inscribed in a circle as shown.

Calculate the angle .

Just write the number.

 

Not drawn accurately.

CORRECT ANSWER
94.5
EDDIE SAYS
a° = 180° - 85.5°
---- OR ----

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