Question

1. in the diagram below, \\( \angle a b d \\) is a straight angle. what is the measure of \\( \angle c b d \\)?

\\( m \angle c b d = \\)
show your work

Explanation:

Step1: Use the property of straight angle

Since \(\angle ABD\) is a straight angle, \(m\angle ABC + m\angle CBD=180^{\circ}\).
Given \(m\angle ABC=(3a - 2)^{\circ}\) and \(m\angle CBD=(5a + 30)^{\circ}\), we have the equation \((3a - 2)+(5a + 30)=180\).

Step2: Simplify the equation

Combine like - terms: \(3a+5a-2 + 30=180\), which simplifies to \(8a+28 = 180\).
Subtract 28 from both sides: \(8a=180 - 28\), so \(8a=152\).
Divide both sides by 8: \(a=\frac{152}{8}=19\).

Step3: Find \(m\angle CBD\)

Substitute \(a = 19\) into \(m\angle CBD=(5a + 30)^{\circ}\).
\(m\angle CBD=5\times19+30\).
First, calculate \(5\times19 = 95\), then \(95+30=125\).

Answer:

\(125\)