Question

partner a

1. m∠abc = 180° solve

Explanation:

Step1: Identify angle - sum relationship

The sum of the angles in \(\angle ABC\) is \(180^{\circ}\), and \(\angle ABC=\angle AOB + \angle BOC\) (where \(O\) is the vertex of the angles at \(B\)). Given \(\angle AOB = 3x^{\circ}\) and \(\angle BOC=40^{\circ}\), we have the equation \(3x + 40=180\).

Step2: Solve the equation for \(x\)

Subtract 40 from both sides of the equation: \(3x=180 - 40\). So \(3x = 140\). Then divide both sides by 3: \(x=\frac{140}{3}\approx46.67\).

Answer:

\(x = \frac{140}{3}\)