EDGE Math 8

Basic Postulates (2)

The Angle Addition Postulate is similar to the Segment Addition Postulate. You can calculate the measures of two angles with a common vertex and a common side but no common interior points by performing addition and subtraction.

Postulate 10. Angle Addition Postulate

If point D is in the interior of

∠ B A C,

then

m ∠ B A C = m ∠ B A D + m ∠ D A C .

Refer to the following figure:

The addition statement $m ∠ B A C = m ∠ B A D + m ∠ D A C$ is equivalent to $m ∠ D A C = m ∠ B A C - m ∠ B A D .$

Using a protractor to measure the angles in the figure, you can check that $m ∠ B A D = 76$ and $m ∠ D A C = 50.$

Using the Angle Addition Postulate, you will get the following:

\begin{array}{l} m ∠ B A C = m ∠ B A D + m ∠ D A C \\ = 76 + 50 \\ = 126 \end{array}

Thus, $∠ B A C$ measures 126°.