Directions: Using the digits from 1 – 9, at most one time each, find the measures of the two angles that form supplementary angles where their difference is as large as possible.
![](https://www.openmiddle.com/wp-content/uploads/2021/05/prob2.png)
Hint
What is the relationship between the angles that form supplementary angles?
Answer
Possible Solutions:
23 and 157
24 and 156
26 and 154
23 and 157
24 and 156
26 and 154
Source: Debra Schneider
The angles that fulfill the criteria are:
123° and 57°, with a difference of 66°
124° and 56°, with a difference of 68°
126° and 54°, with a difference of 72°
127° and 53°, with a difference of 74°
132° and 48°, with a difference of 84°
138° and 42°, with a difference of 96°
142° and 38°, with a difference of 104°
148° and 32°, with a difference of 116°
153° and 27°, with a difference of 126°
154° and 26°, with a difference of 128°
156° and 24°, with a difference of 132°
157° and 23°, with a difference of 134° <– greatest possible difference (even if we included non-leading zeros)
If we allow zero anyhwere, we can add:
083° and 97°, with a difference of 14°
084° and 96°, with a difference of 12°
086° and 94°, with a difference of 8°
087° and 93°, with a difference of 6°
093° and 87°, with a difference of 6°
094° and 86°, with a difference of 8°
096° and 84°, with a difference of 12°
097° and 83°, with a difference of 14°
102° and 78°, with a difference of 24°
104° and 76°, with a difference of 28°
106° and 74°, with a difference of 32°
108° and 72°, with a difference of 36°
172° and 08°, with a difference of 164°
174° and 06°, with a difference of 168°
176° and 04°, with a difference of 172°
178° and 02°, with a difference of 176° <– greatest possible difference