Answer:
Step-by-step explanation:
1) The diagram is a polygon with unequal sides. The number of sides and angles is 5. This means that it is an irregular Pentagon. The formula for the sum of interior angles of a polygon is expressed as
(n - 2)180
Where n is the number if sides of the polygon. Since the number of sides of the given polygon is 5, the sum if the interior angles would be
(5-2)×180 = 540 degrees. Therefore,
10x - 3 + 5x + 2 + 7x - 11 + 13x - 31 + 8x - 19 = 540
43x - 62 = 540
43x = 540 + 62 = 602
x = 602/43 = 14
Angle S = 13 - 31 = 13×14 - 31 = 182 - 31
Angle S = 151 degrees.
4) The diagram is a rectangle. Opposite sides are equal. Triangle JNM is an isosceles triangle. It means that its base angles, Angle NMJ and angle NJM are equal. Therefore
3x + 38 = 7x - 2
7x - 3x = 38 + 2
4x = 40
x = 40/4
x = 10
Angle NMJ = 7x - 2 = 7×10 - 2 = 68 degrees.
Angle JML = 90 degrees ( the four angles in a rectangle are right angles). Therefore,
Angle NML = 90 - 68 = 22 degrees
