# Angle Properties

## Angles at a Point

Angles at a point are the angles formed around a common point, with their vertices coinciding at that point. The sum of angles at a point is always 360°.

• In this case, the sum of all the angles = 136° + 125° + 99° = 360°

This can be useful when solving problems involving angles around a point. For example, if we know three of the four angles formed around a point, we can find the fourth angle by subtracting the sum of the known angles from 360°.

Example:

Suppose we have angles A, B, C and D around point O, with angle A = 100°, angle B = 80°, and angle C = 120°. What is the measure of angle D?

Since the sum of angles at a point is 360°, we can find angle D by subtracting the sum of angles A, B, and C from 360°:

Angle D = 360° – (100° + 80° + 120°)

= 360° – 300°

= 60°

## Angles on a Straight Line

Angles on a straight line are the angles created when two lines meet on a straight path. The point where they connect is called the vertex, and it’s also on the straight line. The sum of angles on a straight line is always 180°.

• Here, the sum of a + b = 103° + 77°

This rule is useful when solving problems involving supplementary angles or when determining the missing angle on a straight line.

Example:

If angle F = 45° and angle E = x, what is the measure of angle E?

Since angle E and angle F lie on a straight line, their sum is equal to 180°

Angle E + Angle F = 180°

x + 45° = 180°

x = 180° − 45° = 135°

So, angle E = 135°