In triangle ABC the measures of its angles are labeled a °, b °, and c °. Ray BD bisects the exterior angle at vertex B. Enter an expression in terms of a and c for the measure of angle CBD.

CBD = 90° + (a° + b°) / 2 We know the following about angle CBD. 1. measurement of interior angle at vertex B is b° 2. measurement of exterior angle at vertex B is (360° - b°) 3. measurement of angle CBD is (360° - b°) / 2 Now what we need to do is determine what b is using just a and c. Since ABC is a triangle and the sum of the interior angles on a triangle add to 180°, we can easily make the following equation b° = 180° - a° - b° So let's substitute that equation for b in the expression in #3 above, giving m = (360° - (180° - a° - b°)) / 2 And simplify m = (360° - (180° - a° - b°)) / 2 m = (360° - 180° + a° + b°) / 2 m = (180° + a° + b°) / 2 m = 90° + (a° + b°) / 2 So the measurement of angle CBD is 90° + (a° + b°) / 2

In tariage Abc the measurs of its angle are labed abc. Ray BD bisect the exterior. angle at vertex B. CBD