Chapter 7, Problem 10RP

To determine

To calculate : The values of CE, $m\angle BCE$ and $m\angle BEC$

Answer to Problem 10RP

The values are $CE=6$ , $m\angle BCE={80}^0$ and $m\angle BEC={60}^0$

Explanation of Solution

Given information : The following information is given

C is the midpoint of BD

E is the midpoint of BF

  $DF=12$

  $m\angle D={80}^0$

  $m\angle B={60}^0$

Formula used : The angles of similar triangles are congruent, and the sides are in the same ratio as the original triangle

Calculation : we know that as C is the midpoint of BD, and E is the midpoint of BF, we can say that CE is parallel to DF. Also, angles are congruent for parallel lines.

Thus, we can say that

  $m\angle BCE=m\angle BDF={80}^0$

Also, $m\angle BEC=m\angle BFD={60}^0$

We know that in similar triangles BDF and BCD,

  $\frac{BC}{BD}=\frac{BE}{BF}=\frac{1}{2}$

Thus, $\frac{CE}{DF}=\frac{1}{2}$ , where $DF=12$

Hence, $CE=6$