the angles of a quadrilateral are 5x - 30° 60 degrees minus x 3x + 60 degrees and 4x + 50 degrees find the smallest of these angles

The smallest of the angles is 60-x

Step-by-step explanation:

Here, given the angles of a quadrilateral, we are told to find the smallest angle

Mathematically, the sum of all these angles add up to be 360

Thus;

5x-30 + 60-x + 3x + 60 + 4x + 50 = 360

Collecting like terms, we have;

5x-x+3x+4x - 30 + 60+60 + 50 = 360

11x + 140 = 360

11x = 360-140

11x = 220

x = 220/11

x = 20 degrees

To know the smallest angle, we plug the value of x in each of the angles

5x - 30 = 5 (20) - 30 = 100-30 = 70

60-x = 60-20 = 40

3x + 60 = 3 (20) + 60 = 60+60 = 120

4x + 50 = 4 (20) + 50 = 80+50 = 130

The smallest is thus 60-x