Chapter 15, Problem 19CR

To determine

To find: the angle of $BE$ .

Answer to Problem 19CR

  $BE={175}^{\circ }$ .

Explanation of Solution

Given:

  

Calculation:

According to the question, there is a circle in which $BD=CE={80}^{{}^0}$ .

The objective is to find $BE$ .

Now, let the angle $CD=x$ Then,

  $\begin{array}{l}80+x+75={180}^{\circ }\\ 155+x={180}^{\circ }\\ x=180-155={25}^{\circ }\end{array}$

Now, in whole circle,

  $\begin{array}{l}BD+DC+CE+BE={360}^{\circ }\\ 80+25+80+BE={360}^{\circ }\\ 185+x={360}^{\circ }\\ x=360-185={175}^{\circ }\end{array}$

Therefore, the angle of $BE={175}^{\circ }$ .