Question

the diagram shows △abc and (overrightarrow{bd}). what is the measure of ∠acd?

Explanation:

Step1: Recall triangle - angle sum property

In right - triangle $ABC$, $\angle ABC = 90^{\circ}$ and $\angle BAC=43^{\circ}$. The sum of the interior angles of a triangle is $180^{\circ}$. So, $\angle ACB=180^{\circ}-\angle ABC - \angle BAC$.
$\angle ACB=180^{\circ}-90^{\circ}-43^{\circ}=47^{\circ}$

Step2: Use linear - pair property

$\angle ACD$ and $\angle ACB$ form a linear pair. A linear pair of angles is supplementary, i.e., $\angle ACD+\angle ACB = 180^{\circ}$.
So, $\angle ACD=180^{\circ}-\angle ACB$.
Substitute $\angle ACB = 47^{\circ}$ into the equation: $\angle ACD=180 - 47=133^{\circ}$

Answer:

$133$