Chapter 9.2, Problem 8PSA

To determine

To find:The measure of arc BC and angle BCA

Answer to Problem 8PSA

The measure of $m\stackrel{⌢}{BC}={130}^0$ and $\angle BCA={25}^0$

Explanation of Solution

Given information:The following information has been given

  $m\stackrel{⌢}{AB}={50}^0$

Formula used:Basic addition and properties of triangles are used.

Calculation:We know that as $m\stackrel{⌢}{AB}={50}^0$ , we will have

  $\angle BOA={50}^0$

Also, angle BOC is supplementary angle to BOA. Thus, we can say that

  $\angle BOC={180}^0-\angle BOA={130}^0$

Now, we know that

  $m\stackrel{⌢}{BC}=\angle BOC={130}^0$

Now, we know that triangle BOC is isosceles with O as the vertex. Hence, we can say that

  $\angle BCA=\frac{{180}^0-\angle BOC}{2}={25}^0$