Answer:
Step-by-step explanation:
1) sum of measures of interior angle 30-gon = 180 * (n - 2) = 180* (30-2)
= 180*28 = 5040
2) measure of one interior angle 30-gon = 5040/30 = 168
3) Interior angle of a regular polygon = 160
Exterior angle of a regular polygon = 180 - 160 = 20
No. of sides = 360/exterior angle = 360/20 = 18 sides
4) m<A = 4x
m<C =7x
5) opposite angles are equal in a parallelogram.
i) 2x + 20 = 4x - 50
20 + 50 = 4x - 2x
70 = 2x
2x = 70
x = 70/2 = 35
x =35
2y - 90 = y
2y - y = 90
y =90
ii)opposite sides are equal in a parallelogram.
6x - 15 = x + 10
6x - x = 10 + 15
5x = 25
x = 25/5
x = 5
4y - 20 = 2y - 8
4y - 2y = 20 - 8
2y = 12
y = 12/2
y = 6
