Question 1105868
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The largest angle has measure n, and one of the other angles has measure n/2.<br>
The sum of all four angles is 360 degrees.<br>
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<br>
{{{n+n+n+n/2 > 360}}}
{{{7n/2 > 360}}}
{{{7n > 720}}}
{{{n > 102.85}}}<br>
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.<br>
So the smallest integer value for n is 104.<br>
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.