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=(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)`