Answer: 54 degrees
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Step-by-step explanation:
Method 1
The exterior angles of any polygon always add to 360 degrees.
3x+8x+9x = 360
20x = 360
x = 360/20
x = 18
Then,
- 3x = 3*18 = 54
- 8x = 8*18 = 144
- 9x = 9*18 = 162
which represent the exterior angles of this triangle.
As a check: 54+144+162 = 360 which confirms we have the correct values.
The smallest exterior angle is therefore 54 degrees
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Method 2
The exterior angles 3x, 8x, and 9x have the corresponding interior angles of 180-3x, 180-8x, and 180-9x in that order.
For any triangle, the interior angles always add to 180 degrees.
angle1+angle2+angle3 = 180
(180-3x)+(180-8x)+(180-9x) = 180
540-20x = 180
-20x = 180-540
-20x = -360
x = -360/(-20)
x = 18
This then leads to 3x = 3*18 = 54 degrees as the final answer.