Circle Theorems (demo)

Question 1

Find the angle marked x.

Answer 1

x = 30 degrees

Properties used:

Vertically opposite angles are equal.

Every angle at the circumference of a semi-circle that is subtended by the diameter of the semi-circle is a right angle.

Angles in a triangle sum to 180 degrees.

Question 1

Find the values of x and y.

Answer 1

x = 80 degrees, y = 100 degrees

Properties used:

The angle at the centre of a circle is twice the angle at the circumference subtended by the same arc.

The sum of opposite angles in a cyclic quadrilateral is 180⁰.

Question 3

Find the angle marked x.

Answer 3

x = 80 degrees

Properties used:

Angles at the circumference in the same segment of a circle are equal.

Every angle at the circumference of a semi-circle that is subtended by the diameter of the semi-circle is a right angle.

Question 4

Find the size of the lettered angles in this circle.

Answer 4

g = 105 degrees, h = 99 degrees

Properties used:

Angles on a straight line sum to 180 degrees.

The sum of opposite angles in a cyclic quadrilateral is 180 degrees.

Question 5

What is the size of angle x?

Answer 5

105 degrees.

Properties used:

The angle at the centre of the circle is twice the angle at the circumference subtended by the same arc.