Chapter 4.3, Problem 19PPS

To determine

To Find: The value of $x$ and $y$ .

Answer to Problem 19PPS

The value of $x=4°$ and $y=2°$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Consider the value of the third angle in the upper triangle is,

  $\begin{array}{c}z=180°-148°-18°\\ =14°\end{array}$

From the congruent pair of the both the triangles.

  $\begin{array}{l}\left(3x+y\right)°=14°\\ 3x+y=14\end{array}$

Then, by angle sum property.

  $\begin{array}{l}\left(5x-y\right)°+\left(3x+y\right)°+148°=180°\\ 8x=32°\\ x=4°\end{array}$

Also,

  $\begin{array}{l}3\left(4°\right)+y=14\\ y=14-12\\ y=2°\end{array}$