Question

7
for the figure below, answer the following questions.
(x + 96)°
5x°
a) what type of angle pairs?
b) find the value of x.

Explanation:

Step1: Identify the angle pair type

The two angles \((x + 96)^{\circ}\) and \(5x^{\circ}\) are adjacent and form a linear - pair. A linear pair of angles is supplementary, meaning their sum is \(180^{\circ}\).

Step2: Set up the equation

Since the angles are supplementary, we have the equation \((x + 96)+5x=180\).

Step3: Simplify the left - hand side of the equation

Combine like terms: \(x+5x + 96=180\), which simplifies to \(6x+96 = 180\).

Step4: Solve for \(x\)

Subtract 96 from both sides: \(6x=180 - 96\). So, \(6x=84\).
Divide both sides by 6: \(x=\frac{84}{6}\).

Answer:

a) Linear pair (supplementary angles)
b) \(x = 14\)