Chapter 2.7, Problem 18PSD

To determine

Argument is to be created to contradict that $m\angle DEB={80}^0$

Answer to Problem 18PSD

The argument is created to contradict the given statement

Explanation of Solution

Given information : The following information has been given

AB and CB intersect at E

  $m\angle AEC:m\angle AED=2:3$

Firstly, we can say that $\angle AEC$ and $\angle AED$ are supplementary angles

Thus, we can say that

  $\angle AEC+\angle AED={180}^0$

Now let $\angle AEC$ be 2x, so $\angle AED$ will be 3x

Now, putting the values of $\angle AEC$ and $\angle AED$ in the equation, we get

  $5x={180}^0\to x={36}^0$

Hence, we get

  $\angle AEC={72}^0$

  $\angle AED={108}^0$

Now, we know that $\angle AEC$ and $\angle DEB$ are vertically opposite angles

Thus, $m\angle DEB=m\angle AEC$

But,

  $m\angle AEC={72}^0$

Hence,

  $m\angle DEB={72}^0$

Therefore, argument is created to contradict that $m\angle DEB={80}^0$