Circle Theorems: Angles in a cyclic quadrilateral
Switch to our new maths teaching resources
Slide decks, worksheets, quizzes and lesson planning guidance designed for your classroom.
Play new resources video
Lesson details
Key learning points
- In this lesson, we will learn that opposite angles in a cyclic quadrilateral sum to 180 degrees. We will prove this result with a general case.
Licence
This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.
Loading...
3 Questions
Q1.
Work out the size of angle x.
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707156475%2Fleq7ocnuvq2mqvckya7q.png&w=640&q=75)
104º
128º
38º
Q2.
Work out the size of angle y.
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707156437%2Fkrtiqsznkgvxcqurntyc.png&w=640&q=75)
147º
57º
66º
Q3.
Work out the size of angle x.
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707156445%2Famqe7p296bnxk0qxn1wm.png&w=640&q=75)
21.5º
86º
90º
3 Questions
Q1.
What can you say about the angles x and y in this diagram?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707206572%2Ftlhzgsmwhnhz4buyfc8j.png&w=640&q=75)
They are both acute angles.
They are both obtuse angles.
They will add together to equal 90º.
Q2.
Work out the size of angle x.
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707206579%2Fnlpw8aacmf4fuv2djagn.png&w=640&q=75)
110º
185º
70º
Q3.
Work out the size of angle y.
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707206590%2Flq7dxwsge6okkgtcigln.png&w=640&q=75)
109º
149º
74º