Question

1. find the values of x and y. (2y + 5)° (5x - 17)° (3x - 11)°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(5x - 17=3x - 11\).
\[

$$\begin{align*} 5x-3x&=- 11 + 17\\ 2x&=6\\ x& = 3 \end{align*}$$

\]

Step2: Use the fact that the sum of angles in a right - angle situation

The angle \((2y + 5)^{\circ}\) and \((3x - 11)^{\circ}\) are complementary (since the angle between the two lines is a right - angle). Substitute \(x = 3\) into \((3x - 11)^{\circ}\), we get \(3\times3-11=9 - 11=-2\) (this is wrong, we should use the fact that the sum of the non - right angles in the right - angled intersection is \(90^{\circ}\)). So, \((2y + 5)+(5x - 17)=90\). Substitute \(x = 3\) into this equation:
\[

$$\begin{align*} 2y+5+(5\times3 - 17)&=90\\ 2y+5+(15 - 17)&=90\\ 2y+5 - 2&=90\\ 2y+3&=90\\ 2y&=87\\ y& = 43.5 \end{align*}$$

\]

Answer:

\(x = 3\), \(y=43.5\)