Question 1

What is an angle that is adjacent to DEA?

Question 2

Answer:

$\large\boxed{\tt \angle CEA, \ and \ \angle BEA.}$

Explanation:

$\textsf{We are asked for an angle that is \underline{Adjacent} to} \ \tt \angle DEA.$

$\large\underline{\textsf{What are Adjacent Angles?}}$

$\textsf{Adjacent Angles are 2 angles that share a common vertex, and line segment (arm).}$

$\textsf{Adjacent Angle don't overlap, however they can be any measure as long as they're}$

$\textsf{angles. \textsf{Note that Adjacent Angles are mainly identified as angles next to each other.}}$

$\large\underline{\textsf{Identifying the Adjacent Angle(s);}}$

$\textsf{Remember that Adjacent Angles don't overlap, which means that} \ \tt \angle DEC \ \textsf{is incorrect.}$

$\tt \angle BEC \ \ \textsf{doesn't share a common line segment with} \ \tt \angle DEA, \ \textsf{hence that angle is incorrect.}$

$\textsf{Adjacent Angles don't overlap, hence} \ \tt \angle DEB \ \textsf{is incorrect.}$

$\underline{\textsf{We are left with 2 options;}}$

$\underline{\textsf{Why are they both correct?}}$

$\textsf{These 2 angles both qualify as Adjacent to} \ \tt \angle DEA. \ \textsf{Both angles share a common}$

$\textsf{side, a common vertex, and both angles don't overlap with} \ \tt \angle DEC. \ \textsf{This means that}$

$\textsf{there are 2 correct options for this problem.}$

$\large\underline{\textsf{Hence;}}$

$\large\boxed{\tt \angle CEA, \ and \ \angle BEA.}$

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