Question

find the measure of angle cdb. explain your reasoning including the postulate you used. find the measure of angle abd. find the measure of angle a.

Answer 1

We get that the triangles ADB and CDB are congruent because of SSS(Side, Side, Side postulate) . So we get that the angles are also congruents

$\begin{gathered} \angle ADB+\angle CDB=72^{\circ} \\ \end{gathered}$

But ADB and CDB are the same so

$\angle CDB=\frac{72}{2}=36^{\circ}$$\begin{gathered} \angle ABD=\angle CBD \\ 2\angle CBD=180 \\ \angle CBD=90^{\circ} \end{gathered}$

The angle A is equal to

$\angle A=180-90-36=54^{\circ}$