Chapter 10.7, Problem 9PSB

a.

To determine

Find angle $\angle ADC$ .

Answer to Problem 9PSB

  $\angle ADC=65°$

Explanation of Solution

Given information:

  

  $\angle B=115°,\stackrel{⌢}{AD}=60°,\overline{BC}\left|\right|\overline{EF}$ .

Calculation:

It is given that, $\angle B=115°,\stackrel{⌢}{AD}=60°,\overline{BC}\left|\right|\overline{EF}$

  $\begin{array}{l}\angle ADC=\frac{360°-\left(115°\right)\left(2\right)}{2}\\ \angle ADC=\frac{360°-\left(230°\right)}{2}\\ \angle ADC=65°\end{array}$

Hence , $\angle ADC=65°$ .

b.

To determine

Find angle $\angle CDF$ .

Answer to Problem 9PSB

  $\angle CDF=85°$

Explanation of Solution

Given information:

  

  $\angle B=115°,\stackrel{⌢}{AD}=60°,\overline{BC}\left|\right|\overline{EF}$ .

Calculation:

It is given that, $\angle B=115°,\stackrel{⌢}{AD}=60°,\overline{BC}\left|\right|\overline{EF}$

  $\begin{array}{l}\angle CDF=\frac{\left(115°\right)\left(2\right)-60°}{2}\\ \angle CDF=\frac{230°-60°}{2}\\ \angle CDF=85°\end{array}$

Hence , $\angle CDF=85°$ .

c.

To determine

Find angle $\angle C$ .

Answer to Problem 9PSB

  $\angle C=85°$

Explanation of Solution

Given information:

  

  $\angle B=115°,\stackrel{⌢}{AD}=60°,\overline{BC}\left|\right|\overline{EF}$ .

Calculation:

It is given that, $\angle B=115°,\stackrel{⌢}{AD}=60°,\overline{BC}\left|\right|\overline{EF}$

  $BC\left|\right|EF$ opposite angles are congruent,

  $\angle C=85°$

Hence , $\angle C=85°$ .

d.

To determine

Find angle $\angle A$ .

Answer to Problem 9PSB

  $\angle A=95°$

Explanation of Solution

Given information:

  

  $\angle B=115°,\stackrel{⌢}{AD}=60°,\overline{BC}\left|\right|\overline{EF}$ .

Calculation:

It is given that, $\angle B=115°,\stackrel{⌢}{AD}=60°,\overline{BC}\left|\right|\overline{EF}$

sum of quadrilateral angles are $360°$ so that,

  $\begin{array}{l}\angle A=360°-\left(115°+65°+85°\right)\\ \angle A=95°\end{array}$

Hence , $\angle A=95°$ .