Question

in the diagram, which angles are vertical angles? choose two correct answers

treca applied geometry - 222
linear pairs and vertical angles

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are the angles opposite each other when two lines cross.

Step2: Analyze each pair

• For \(\angle ABE\) and \(\angle EBD\): They form a linear - pair (sum to \(180^{\circ}\)), not vertical angles.
• For \(\angle ABC\) and \(\angle CBD\): They form a linear - pair (sum to \(180^{\circ}\)), not vertical angles.
• For \(\angle ABC\) and \(\angle EBD\): When two lines \(AD\) and \(EC\) intersect at point \(B\), \(\angle ABC\) and \(\angle EBD\) are opposite each other.
• For \(\angle ABE\) and \(\angle ABC\): They are adjacent angles, not vertical angles.

Answer:

\(\angle ABC\) and \(\angle EBD\)