SOLUTION: Each of a quadrilateral's interior triangle measures, in degrees, is an integer. The least and greatest of these measures are in the ratio 1:2. Let the greatest of these measures b
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Question 1105868: Each of a quadrilateral's interior triangle measures, in degrees, is an integer. The least and greatest of these measures are in the ratio 1:2. Let the greatest of these measures be n degrees. What is the greatest possible value of n? Answer by greenestamps(13214) (Show Source):
The largest angle has measure n, and one of the other angles has measure n/2.
The sum of all four angles is 360 degrees.
Since n is the measure of the largest angle, the other two angles have measures less than n. Suppose that the two other angles had measure n; then we would know that the sum of the four angles is greater than 360 degrees. So
The smallest integer that satisfies this inequality is 103. But that would make the other given angle 51.5, and the degree measures of all four angles have to be integers.
So the smallest integer value for n is 104.
That makes the two given angles 104 and 52, for a sum of 156. Then the sum of the other two angles is 204; they can be either 102 and 102, or 101 and 103.
