Question

angle measure correct?

m∠abd 120

m∠dbc ny

m∠abe ny

m∠cbe ny

m∠abd + m∠dbc + ∠abe + ∠ebc ny

Explanation:

Step1: Find \(m\angle DBC\)

\(\angle ABD\) and \(\angle DBC\) are supplementary (form a linear pair). So \(m\angle ABD + m\angle DBC=180^{\circ}\). Given \(m\angle ABD = 120^{\circ}\), then \(m\angle DBC=180 - 120=60^{\circ}\).

Step2: Find \(m\angle ABE\)

\(\angle ABD\) and \(\angle ABE\) are vertical angles. Vertical angles are equal. So \(m\angle ABE=m\angle DBC = 60^{\circ}\).

Step3: Find \(m\angle CBE\)

\(\angle CBE\) and \(\angle ABD\) are vertical angles. Vertical angles are equal. So \(m\angle CBE = 120^{\circ}\).

Step4: Find \(m\angle ABD+m\angle DBC+\angle ABE+\angle EBC\)

Substitute the values: \(120 + 60+60 + 120=360^{\circ}\) (the sum of angles around a point is \(360^{\circ}\)).

Answer:

\(m\angle DBC = 60^{\circ}\), \(m\angle ABE=60^{\circ}\), \(m\angle CBE = 120^{\circ}\), \(m\angle ABD+m\angle DBC+\angle ABE+\angle EBC = 360^{\circ}\)