Question

which are linear pairs? check all that apply
∠dae and ∠ead
∠bac and ∠cad
∠bae and ∠ead
∠ead and ∠dac
∠cae and ∠bad

Explanation:

Step1: Recall the definition of a linear pair

A linear pair of angles is a pair of adjacent angles whose non - common sides are opposite rays and whose sum is \(180^{\circ}\).

Step2: Analyze each option

• For \( \angle DAE\) and \( \angle EAD\): These are the same angle, not a pair of distinct angles forming a linear pair.
• For \( \angle BAC\) and \( \angle CAD\): They are adjacent angles and their non - common sides \(AB\) and \(AD\) are opposite rays (since \(B\), \(A\), \(D\) are collinear in a straight - line sense from the figure's structure). Also, \(m\angle BAC + m\angle CAD=180^{\circ}\) (as they form a straight angle at point \(A\)).
• For \( \angle BAE\) and \( \angle EAD\): Their non - common sides are not opposite rays.
• For \( \angle EAD\) and \( \angle DAC\): They are adjacent angles. Their non - common sides \(AE\) and \(AC\) are opposite rays (since \(C\), \(A\), \(E\) are collinear in a straight - line sense from the figure's structure). Also, \(m\angle EAD + m\angle DAC = 180^{\circ}\) (as they form a straight angle at point \(A\)).
• For \( \angle CAE\) and \( \angle BAD\): They are not adjacent angles.

Answer:

B. \( \angle BAC \) and \( \angle CAD \), D. \( \angle EAD \) and \( \angle DAC \)