Question

What is an angle that is supplementary to CDH?

Answer 1

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

Explanation:

`\textsf{We are asked to find an angle that is \underline{supplementary} to} \ \tt \angle CDH.`

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

`\textsf{Supplementary Angles are 2 or more angles that form a straight angle, or a 180}^(\circ)`

`\textsf{angle. We can identify supplements by looking at the line segments that form these}`

`\textsf{angles, or by the measures of their angles. Note that Supplementary Angles are}`

`\textsf{also considered as Linear Pairs, where they too also form a straight angle.}`

`\textsf{*Note that Supplements are Linear Pairs if they share a common`

`\large\underline{\textsf{Identifying the Supplement;}}`

`\textsf{Remember that we are asked to find the supplement of} \ \tt \angle CDH. \ \textsf{This diagram can be}`

`\textsf{simpler if we mainly focus on the angles sharing the line} \ \overleftrightarrow{\tt FI}. \ \textsf{We now should have}`

`\textsf{2 possible angles that are supplements;} \ \tt \angle FCG \ and \ \angle IDH. \ \textsf{As we can likely identify,}`

`\tt \angle CDH \ \textsf{is an Obtuse Angle as it exceeds the measure of a Right Angle, but still is}`

`\textsf{less than the measure of a Straight Angle. Because} \ \tt \angle FCJ \ \textsf{isn't related to} \ \tt \angle CDH \ \textsf{in}`

`\textsf{any way, this means that there is only one option which is} \ \tt \angle IDH. \ \textsf{This angle is}`

`\textsf{a Supplement and a Linear Pair of} \ \tt \angle CDH \ \textsf{as they both share a common line segment.}`

`\textsf{Looking at} \ \overrightarrow{\tt CI} \ \textsf{it's also clear that} \ \tt \angle IDH \ \textsf{shares a line with} \ \tt \angle CDH.`

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

`\large\boxed{\tt \angle IDH} \ \textsf{\small is a supplement to} \ \tt \angle CDH.`