Question 1105740
<br>
The sum of the measures of the angles of a trapezoid is 360 degrees.<br>
If the trapezoid is ABCD with bases BC and AD, then the sum of the measures of angles A and B is 180 degrees, and the sum of the measures of angles C and D is 180 degrees.<br>
There are three cases for the problem....<br>
(1) Angles A and B are 3x and 5x; that makes the other two angles 7x and x.
{{{7x+x = 8x = 180}}}  -->  x = 22.5; the fourth angle is 22.5 degrees.<br>
(2) Angles A and B are 3x and 7x; that makes the other two angles 5x and 5x.
{{{5x+5x = 10x = 180}}}  -->  x = 18; the fourth angle is 5x = 90 degrees.
(3) Angles A and B are 5x and 7x; that makes the other two angles 3x and 9x.
{{{3x+9x = 12x = 180}}}  -->  x = 15; the fourth angle is 9x = 135 degrees.