Question

2 lines intersect at point A. One line contains points C, A, E and the other line contains points B, A, D.
Which are linear pairs? Check all that apply.

∠DAE and ∠EAD
∠BAC and ∠CAD
∠BAE and ∠EAD
∠EAD and ∠DAC
∠CAE and ∠BAD

Answer 1

Linear pair = two adjacent angles with a common side whose other sides are opposite rays (sum to 180°).

Given C, A, E collinear (so AC and AE are opposite rays) and B, A, D collinear (so AB and AD are opposite rays).

Check each:
- ∠DAE and ∠EAD: these are the same angle (both use AD and AE) → not a linear pair.
- ∠BAC and ∠CAD: share AC; noncommon rays AB and AD are opposite → linear pair.
- ∠BAE and ∠EAD: share AE; noncommon rays AB and AD are opposite → linear pair.
- ∠EAD and ∠DAC: share AD; noncommon rays AE and AC are opposite → linear pair.
- ∠CAE and ∠BAD: do not share a common side (each is a straight angle on its own) → not a linear pair.

So the linear pairs are: ∠BAC & ∠CAD, ∠BAE & ∠EAD, and ∠EAD & ∠DAC.