Question

Find the measure of angle CDB. Explain your reasoning, including the theorem or postulate you used. (2 pts.) b) Find the measure of angle. (1 pt.)

Answer 1

The triangle is isosceles, since two of its sides are equal. Besides, the little triangles ABD and CBD are congruent and this can be concluding using the criterion SSS , since they share one side, and the other sides are equal. Then the angles are congruent, and the angles ADB and CDB are congruent and have the same measure. Then

`\begin{gathered} m\angle ADB+m\angle CDB=m\angle ADC \\ 2m\angle CDB=m\angle ADC \\ m\angle CDB=(72)/(2) \\ m\angle CDB=32 \end{gathered}`

Then, the measure of angle CDB is 32 degrees.