Question

Which angle is complementary to CDA?

Answer 1

`\large\boxed{\tt \angle CDB \ is \ Complementary \ to \ \angle CDA.}`

Explanation:

`\textsf{We are asked for the angle that is Complementary to} \ \tt \angle CDA.`

`\textsf{Note that} \ \tt \angle BDA \ \textsf{has an angle marking of a box, meaning that it equals 90}^(\circ). \ \textsf{This}`

`\textsf{means that 2 angles in that right angle will be \underline{Complementary}.}`

`\large\underline{\textsf{What are Complementary Angles?}}`

`\textsf{Complementary Angles are 2 angles that form a 90}^(\circ) \ \textsf{angle. When identifying these}`

`\textsf{angles, both have measures less than 90}^(\circ). \ \textsf{Note that Complementary Angles do \underline{not}}`

`\textsf{have to be \underline{adjacent}.}`

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

`\textsf{Adjacent Angles are 2 or more angles that share a \underline{common vertex}. For our}`

`\textsf{problem, the common vertex is} \ \overrightarrow{\tt DC}.`

`\textsf{While there are 3 angles in total, we are looking for the angle Complementary to}`

`\tt \angle CDA. \ \textsf{This means that} \ \tt \angle BDA \ \textsf{is incorrect. This leaves} \ \tt \angle CDB. \ \textsf{This angle shares}`

`\textsf{a common vertex with} \ \tt \angle CDA.`

`\underline{\textsf{Hence;}}`

`\large\boxed{\tt \angle CDB \ is \ Complementary \ to \ \angle CDA.}`