Angles in an Isosceles Triangle

Angles in an Isosceles Triangle

An isosceles triangle has two equal sides, and the angles opposite those sides are also equal. These equal angles are often called the base angles.

1) Identify the equal angles

Look for the two sides marked as equal. The angles across from them must have the same measure.

2) Use the triangle angle sum

The three interior angles of any triangle add up to 180°. So if the two equal angles are each (x), and the third angle is known, write an equation such as:

[ x + x + \text{known angle} = 180 ]

Then solve for (x).

3) If one base angle is known

If one of the equal angles is given, the other equal angle has the same measure. If the vertex angle is known, subtract it from 180° and divide the remainder by 2.

4) Check your answer

Make sure:

• the two equal angles really match,
• all three angles add to 180°,
• your final answer is simplified.

Quick example method

If the vertex angle is 40°: [ \text{two equal angles} = 180 - 40 = 140 ] [ \text{each base angle} = 140 \div 2 = 70^ ]

So the key steps are: find the equal angles, use the 180° total, and verify the sum.