Chapter 4.2, Problem 47HP

To determine

To calculate:

Missing measures of the given figure.

Answer to Problem 47HP

Missing measures of the given figure is $a=70,b=55,c=55$ .

Explanation of Solution

Given information:

  

Calculation:

The $a°$ and the $110°$ angle are supplementary, because they form a linear pair.

Set $a$ equal to $180-110$

  $\begin{array}{l}a=180-110\\ a=70\end{array}$

The $b°$ angle and $c°$ angle are congruent, because each of the twoangles I smarked with one arc.

Thus, $b=c$

Set $b+c$ equal to $110$

  $\begin{array}{l}b+c=110\\ b+b=110\\ 2b=110\end{array}$

Multiply each side by $\frac{1}{2}$ in above equation,

  $\begin{array}{l}b=110\left(\frac{1}{2}\right)\\ b=55\end{array}$

Thus,

  $\begin{array}{l}c=b\\ c=55\end{array}$ .

Hence, value of measure in given figure is $a=70,b=55,c=55$ .