Chapter 9.5, Problem 19WE

To determine

To calculate: The unknown angles.

Answer to Problem 19WE

  $x=80°$ and $m\angle D=20°$

Explanation of Solution

Given information: $m\angle A=x,m\angle B=2x$ and $m\angle C=x+20$

Formula used: We know the sum of the opposite angles of a quadrilateral inscribed in a circle is $180°$ . We can write $m\angle A+m\angle C=180°$ and $m\angle B+m\angle D=180°$

Calculation: Using the above relation.

  

Plugging the given value we get,

  $\begin{array}{l}m\angle A+m\angle C=180°\\ x+x+20=180\\ 2x=180-20\\ 2x=160\\ x=\frac{160}{2}\\ x=80°\end{array}$

And

  $\begin{array}{l}m\angle B+m\angle D=180°\\ 2x+m\angle D=180\\ 2\times 80+m\angle D=180\\ m\angle D=180-160\\ m\angle D=20°\end{array}$