Question

ABCD is a quadrilateral. If angle A is 10 degrees more than angle B; angle B is 10 degrees more than angle C; and angle C is 10 degrees more than angle D, find each angle.

Answer 1

Answer:

Let the angle D be x

Angle C = x + 10

Angle B = (x + 10) + 10 = x + 20

Angle A = (x + 10 + 10) + 10 = x + 30

Sum of all sides = 360

x+x+10+x+20+x+30 = 360

4x + 60 = 360

4x = 360-60

x = 300/4

x = 75

Angle A = x + 30

= 75 + 30

= 105 degrees

Angle B = x + 20

= 75 + 20

= 95 degrees

Angle C = x + 10

= 75 + 10

= 85 degrees

Angle D = 75 degrees