Question

find the value of x.
the measure of an angle is 69°. what is the measure of its supplementary angle?

Explanation:

Step1: Find the measure of the angle adjacent to \(153^{\circ}\)

Since adjacent angles on a straight line sum to \(180^{\circ}\), the angle adjacent to \(153^{\circ}\) is \(180 - 153=27^{\circ}\)

Step2: Set up an equation for the sum of angles around a point

The sum of angles around a point is \(360^{\circ}\). But since \(LN\) is a straight line (sum \(180^{\circ}\)), we have \(5x + 12x+27 = 180\)
Combine like - terms: \(17x+27 = 180\)
Subtract \(27\) from both sides: \(17x=180 - 27\), so \(17x = 153\)
Divide both sides by \(17\): \(x=\frac{153}{17}\)

Answer:

\(9\)