Question

put your answer in the box.

\\( \angle b a d = \\)

\\( \angle e a d = \\)

\\( \angle b a c = \\)

Explanation:

Step1: Find \(\angle BAD\)

Vertical angles are equal. \(\angle BAD\) and the \(65^{\circ}\) angle are vertical angles. So \(\angle BAD = 65^{\circ}\)

Step2: Find \(\angle EAD\)

\(\angle EAD+\angle BAD = 180^{\circ}\) (linear - pair of angles). Let \(\angle EAD=x\). Then \(x + 65^{\circ}=180^{\circ}\), so \(x=\angle EAD=180^{\circ}- 65^{\circ}=115^{\circ}\)

Step3: Find \(\angle BAC\)

\(\angle BAC+\angle BAD = 180^{\circ}\) (linear - pair of angles). Let \(\angle BAC = y\). Then \(y+65^{\circ}=180^{\circ}\), so \(y=\angle BAC = 115^{\circ}\)

Answer:

\(\angle BAD = 65^{\circ}\), \(\angle EAD = 115^{\circ}\), \(\angle BAC=115^{\circ}\)