Chapter 8.5, Problem 47E

(a)

To determine

To diagram: Sketch the given situations.

Explanation of Solution

Given information: The $\angle ABX$ is 12 more than four times of $\angle CBX$ and $\angle ABC=92°$

Sketch: According to the Angle Addition Postulate, if P is in the interior of $\angle RST$ , so,

  $\angle RST=\angle RSP+\angle PST$

Hence, the required diagram will be as follows:

  

(b)

To determine

To find: The value of angle $\angle ABX\&\angle CBX$ .

Answer to Problem 47E

The values of angle $\angle ABX\&\angle CBX$ are $76°\&16°$ , respectively,

Explanation of Solution

Given information: The $\angle ABX$ is 12 more than four times of $\angle CBX$ and $\angle ABC=92°$

Calculation: Let $\angle CBX$ be as $y°$ then $\angle ABX$ will be as $\left(4y+12\right)°$ .

According to the Angle Addition Postulate,

  $\begin{array}{l}\angle CBX+\angle ABX=\angle ABC\\ y°+\left(4y+12\right)°=92°\\ 5y°=92°-12°\\ y°=\frac{80}{5}\\ y°=16°\\ \therefore \angle CBX=16°\end{array}$

Substitute $y°=16°$ into $\left(4y+12\right)°$ to get $\angle ABX$ ,

  $\begin{array}{l}\angle ABX=\left(4y+12\right)°\\ \angle ABX=\left(4\times 16°+12\right)°\\ \angle ABX=64°+12°\\ \angle ABX=76°\end{array}$