Question

11.
(7x - 23)°
49°
(3x)°
(11y - 1)°
l
m

Explanation:

Step1: Find the value of \(x\)

Since \(7x - 23\) and \(3x+49\) are vertical angles, they are equal.

$$7x - 23=3x + 49$$

$$7x-3x=49 + 23$$

$$4x=72$$

$$x = 18$$

Step2: Find the value of \(y\)

First, find the measure of the angle \(3x\). Substitute \(x = 18\) into \(3x\), we get \(3\times18=54^{\circ}\).
Since \(11y-1\) and \(3x\) are vertical angles, \(11y-1 = 3x\). Substitute \(x = 18\) into the equation:

$$11y-1=54$$

$$11y=54 + 1$$

$$11y=55$$

$$y = 5$$

Answer:

\(x = 18\), \(y = 5\)