Question

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

Explanation:

Step1: Use the property of a straight - angle

Since \(A\), \(B\), and the point on the extension of \(AB\) form a straight - line, \(\angle ABC+\angle CBD = 180^{\circ}\). So, \((3a - 2)+(5a + 30)=180\).

Step2: Solve the equation for \(a\)

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

Step3: Find the measure of \(\angle CBD\)

Substitute \(a = 19\) into the expression for \(\angle CBD\) (\(5a + 30\)).
\(m\angle CBD=5\times19+30\).
First, calculate \(5\times19 = 95\).
Then, \(95+30=125\).

Answer:

\(125^{\circ}\)