Step-by-step Step-by-step explanation:
Let's assume that:
Angle A = 3x
Angle B = (2x + 5)
Angle C = (3x - 10)
Angle D = 2x + 15
Sum of all four angles of quadrilateral = 360°
3x + 2x + 5 + 3x - 10 + 2x + 15 = 360
5x + 5 + 3x - 10 + 2x + 15 = 360
10x + 5 - 10 + 15 = 360
10x -5 + 15 = 360
10x + 10 = 360
10x = 360 - 10
10x = 350
x = 350/10
x = 35°
Now substitute the value of x = 35 in all the angles:
Angle A = 3x = 3(35) = 105°
Angle B = (2x + 5)
= 2(35) + 5 = 70 + 5 = 75°
Angle C = (3x - 10)
= 3(35) - 10 = 105 - 10 = 95°
Angle D = 2x + 15
= 2(35) + 15 = 70 + 15 = 85°
The angles are the quadrilateral are 105°, 75°, 95° and 85°