Question

the diagram shows △abc and bd⃗. what is the measure of ∠acd?

Explanation:

Step1: Recall triangle - angle sum property

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

Step2: Calculate $\angle ACB$

$\angle ACB=180^{\circ}-\angle A - \angle B$. Substituting $\angle A = 43^{\circ}$ and $\angle B = 90^{\circ}$, we get $\angle ACB=180^{\circ}-43^{\circ}-90^{\circ}=47^{\circ}$.

Step3: Use linear - pair property

$\angle ACD$ and $\angle ACB$ form a linear pair. A linear pair of angles is supplementary, i.e., $\angle ACD+\angle ACB = 180^{\circ}$.

Step4: Calculate $\angle ACD$

$\angle ACD=180^{\circ}-\angle ACB$. Since $\angle ACB = 47^{\circ}$, then $\angle ACD=180^{\circ}-47^{\circ}=133^{\circ}$.

Answer:

$133$