Chapter 6.6, Problem 65HP

To determine

The error in the solutions of Bedagi and Belinda.

Answer to Problem 65HP

Belinda is correct.

Explanation of Solution

Given:

The given solutions are:

  

The given figure is:

  

Calculation:

In a kite, there is exactly one pair of angles is congruent.

  

According to Kite Theorem;

  $\angle D\cong \angle B\text{.}$

So,

  $\begin{array}{l}m\angle D=m\angle B\\ m\angle D=100\end{array}$

The sum of all the angles of quadrilateral is 360.

  $\begin{array}{l}m\angle A+m\angle B+m\angle C+m\angle D=360\\ m\angle A+100+45+100=360\\ m\angle A=360-245\\ m\angle A=115\end{array}$

Hence, Belinda is correct.