Triangle Angle Sum Math Example 2

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Example 2

medium
In an isosceles triangle, the vertex angle is 40°40°. Find the two base angles.

Solution

  1. 1
    Step 1: In an isosceles triangle, the two base angles are equal. Let each base angle be bb.
  2. 2
    Step 2: Apply the Triangle Angle Sum: 40°+b+b=180°40° + b + b = 180°.
  3. 3
    Step 3: Simplify: 40°+2b=180°40° + 2b = 180°, so 2b=140°2b = 140°, giving b=70°b = 70°.
  4. 4
    Step 4: Each base angle is 70°70°. Check: 40°+70°+70°=180°40° + 70° + 70° = 180°. ✓

Answer

Each base angle is 70°70°.
An isosceles triangle has two equal sides, and the angles opposite those equal sides (the base angles) are equal. Combined with the angle sum property, knowing the vertex angle determines both base angles. This is one of the most common triangle problems.

About Triangle Angle Sum

The three interior angles of any triangle always sum to exactly 180°180°, so knowing two angles determines the third.

Learn more about Triangle Angle Sum →

More Triangle Angle Sum Examples

Example 1 easy

A triangle has angles [formula] and [formula]. Find the third angle.

Example 3 easy

Can a triangle have angles of [formula], [formula], and [formula]? Justify your answer.

Example 4 hard

In [formula], [formula], [formula], [formula]. Find all three angles.

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