What is an angle that is supplementary to CDH?

Question 1

Question 2

Answer:

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

Explanation:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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