# KS4. Geometry. Angles & Symmetry. Basic angle properties & angles in a triangle

An angle is a measure of turn. We measure turn in degrees, where 360º is a complete turn.

• An angle less than 90º is called an acute angle;
• an angle of exactly 90º is called a right angle;
• an angle of greater than 90º but less than 180º is called an obtuse angle;
• an angle of 180º is called a straight angle (it is a straight line); and
• an angle greater than 180º but less than 360º is called a reflex angle.

We can use this information to identify the value of missing angles. Let’s try it out in the following short exercise (exercise 4 from pages 5 and 6 of the core textbook):

Examples: Let’s come up to the board individually to try some of these:

Calculate the size of the missing angles:

Exercise

Below are the answers:

Triangles

There are four important things that we should know about the angles in triangles:

• In all triangles, the three angles have a sum of 180º;
• In equilateral triangles all of the angles are equal (so they are each 60º);
• In isosceles triangles, each of the two angles between unequal sides is equal;
• The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Example: Find the missing angles

Exercise: Let’s complete exercise 5 on pages 6 and 7 of the core textbook:

Below are the answers: