Year 8 Interactive Maths - Second Edition

Vertically Opposite Angles

Recall that:

Vertically opposite angles are the angles that are opposite to each other, and these angles are equal.

Example 5

Use the information given in the diagram to find x and y.  Give reasons for your answers.

Solution:

Angles Forming a Circle

Recall that:

The sum of all angles that meet at a point is equal to 360º.

There are 360º in one complete revolution.  So, the sum of the angles with a common vertex is equal to 360º.

In the diagram, angles a, b, c and d form a circle with a common vertex.  So:

a + b + c + d = 360º

Example 6

Use the information given in the diagram to find x.  Give reasons for your answer.

Solution:

So, the value of x is 205.

Key Terms

vertically opposite angles, angles forming a circle