Chapter 6.6, Problem 4ACYP

To determine

To calculate: To find measure of $\angle ADC$

Answer to Problem 4ACYP

  $\angle ADC=136$

Explanation of Solution

Given: Figure is as follows:

  

Calculation:

Figure is given as follows:

  

In above figure, given that

  $AB=AD$ and $CB=CD$

Consider triangle ABD

Since $AB=AD$

Thus, $\angle ABD=\angle ADB$ (angles opposite to equal sides are equal)

Also,

  $\begin{array}{l}\angle ABD+\angle ADB+\angle BAD=180\\ 2\angle ADB+38=180\\ 2\angle ADB=142\\ \angle ADB=71\end{array}$

Consider triangle CBD

Since $CB=CD$

Thus, $\angle CBD=\angle CDB$ (angles opposite to equal sides are equal)

Also,

  $\begin{array}{l}\angle CBD+\angle CDB+\angle BCD=180\\ 2\angle CDB+50=180\\ 2\angle CDB=130\\ \angle CDB=65\end{array}$

Now, $\angle ADC$ is calculated as follow:

  $\begin{array}{l}\angle ADC=\angle ADB+\angle CDB\\ \angle ADC=71+65\\ \angle ADC=136\end{array}$

Conclusion:

Hence, $\angle ADC=136$