Question

1. in the diagram below, ∠abd is a straight angle. what is the measure of ∠cbd?

m∠cbd =

Explanation:

Step1: Use the property of a straight angle

Since \(\angle ABD\) is a straight angle (\(180^{\circ}\)), we have \((3a - 2)+(5a + 30)=180\).
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: \(a=\frac{152}{8}=19\).

Step2: Find the measure of \(\angle CBD\)

The measure of \(\angle CBD=(5a + 30)^{\circ}\).
Substitute \(a = 19\) into the expression: \(5\times19+30\).
First, calculate \(5\times19 = 95\), then \(95+30=125\).

Answer:

\(125\)