Question

identifying linear pairs
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 \(\angle DAE\) and \(\angle EAD\)

These are the same angle, not a pair of distinct angles. So, they are not a linear pair.

Step3: Analyze \(\angle BAC\) and \(\angle CAD\)

The non - common sides of \(\angle BAC\) and \(\angle CAD\) are opposite rays (\(AB\) and \(AD\) are not opposite rays). Let's check using the ray concept. The sum of \(\angle BAC+\angle CAD=\angle BAD
eq 180^{\circ}\) (from the figure's ray structure).

Step4: Analyze \(\angle BAE\) and \(\angle EAD\)

The non - common sides of \(\angle BAE\) and \(\angle EAD\) are not opposite rays.

Step5: Analyze \(\angle EAD\) and \(\angle DAC\)

The non - common sides of \(\angle EAD\) and \(\angle DAC\) are opposite rays (\(AE\) and \(AC\) are opposite rays). Also, \(\angle EAD+\angle DAC = 180^{\circ}\) (since they form a straight line at point \(A\)).

Step6: Analyze \(\angle CAE\) and \(\angle BAD\)

The non - common sides of \(\angle CAE\) and \(\angle BAD\) are not adjacent in the linear - pair sense. \(\angle CAE\) is formed by rays \(CA\) and \(AE\), and \(\angle BAD\) is formed by rays \(BA\) and \(AD\).

Answer:

\(\angle EAD\) and \(\angle DAC\)