Question

Which angle is adjacent to ADB?

Answer 1

`\large\boxed{\tt \angle ADC}`

Explanation:

`\textsf{We are asked for which angle is \underline{Adjacent} to} \ \tt \angle ADB.`

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

`\textsf{Adjacent Angles are 2 angles that share a common vertex. These angles are}`

`\textsf{referred to as angles next to each other. Note that it's only possible for an angle to}`

`\textsf{be Adjacent with another angle if both angle share a common vertex.}`

`\textsf{Consider noting as well that Adjacent Angles always have to have a common line}`

`\textsf{segment. This means that one 'arm' of an angle has to be an arm of another.}`

`\textsf{*Adjacent Angles don't overlap!}`

`\underline{\textsf{Review of what a Vertex is;}}`

`\textsf{A Vertex is an intersection point mainly created by lines, or line segments.}`

`\large\underline{\textsf{Identifying the Adjacent Angle;}}`

`\textsf{Our focus should be on} \ \tt \angle ADB. \ \textsf{We are trying to find the Adjacent Angle of} \ \tt \angle ADB.`

`\textsf{We have 2 options to choose from, and they are;} \ \tt \angle ADC \ or \ \measuredangle BCD.`

`\tt \measuredangle BDC \ \textsf{is a Right Angle, and is greater than} \ \tt \angle ADB. \ \textsf{Hence,} \ \tt \angle BDC \ \textsf{is incorrect.}`

`\textsf{This leaves our final, and correct option;} \ \tt \angle ADC.`

`\tt \angle ADB \ and \ \angle ADC \ \textsf{are Adjacent Angle for multiple reasons. Note that these angles}`

`\textsf{are next to each other, they share the same Vertex point, and they share a common}`

`\textsf{side/arm which is} \ \overrightarrow{\tt DA}.`