Angles in a Triangle

A triangle has three sides and three angles.

The angles in a triangle always add up to 180º.

Higher students: the number of degrees in a triangle can be derived using Alternate Angles:

Angles at A and B (blue) are alternate angles;

Angles at A and C (red) are alternate angles;

Angles at A (blue, white and red) are on a straight line = 180º;

Therefore the number of degrees in a triangle is 180.

Determining that a triangle has 180 degrees

Example 1

What is the size of angle A?

Missing angle in a scalene triangle

There are 180º in a triangle. Subtract the other angles from 180 for the answer: 180 - 62 - 33 = 85º

Answer: 85º

Example 2

What is the size of angle B?

Missing angle in an isosceles triangle

It is an Isosceles triangle. Two sides of the triangle are the same length (shown by the marks on two of the lines); therefore two angles also have the same value.

The angle that is given is the odd one out. Subtract this from 180º: 180 - 28 = 152º. Divide this by 2 for the value of B: 152 ÷ 2 = 76º

Answer: 76º