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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.
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