The given figure is a polygon with 4 sides. The sum of the interior angles in a polygon is expressed as
(n - 2)180
Where
n represents the number of sides. Given that n = 4, then the sum of the interior angles in the polygon would be
(4 - 2)180 = 2 * 180 = 360 degrees
Thus, we have
4x + 9 + 7x - 5 + 2x + 15 + 5x - 1 = 360
Collecting like terms, we have
4x + 7x + 2x + 5x + 9 - 5 + 15 - 1 =360
18x + 18 = 360
18x = 360 - 18 = 342
x = 342/18
x = 19
To find the measure of each angle, we would substitute x = 19 into each of the angles. Thus, we have
Angle G = 4 * 19 + 9 = 76 + 9 = 85 degrees
angle B = 2 * 19 + 15 = 38 + 15 = 53 degrees
angle M = 5 * 19 - 1 = 95 - 1 = 94 degrees
angle L = 7 * 19 - 5 = 133 - 5 = 128 degrees