Find the measures of the angles of a quadrilateral if one of them is greater than the second

Find the measures of the angles of a quadrilateral if one of them is greater than the second, third and fourth by 10.20 and 30 degrees

1. Let’s denote the angle A of the quadrangle ABCD as x °.

Then, according to the condition of the problem, angle B = x + 10 °, angle C = x + 20 °, angle D = x + 30 °.

2. We know that the sum of the angles of any quadrangle is 360 °, so we can write the equation

x + (x + 10 °) + (x + 20 °) + (x + 30 °) = 360 °;

4 x + 60 ° = 360 °;

4 x = 360 ° – 60 ° = 300 °;

x = 75 °.

Now you can calculate what the other angles are equal to.

angle B = 75 ° + 10 ° = 85 °,

angle С = 75 ° + 20 ° = 95 ° b

angle D = 75 ° 30 ° = 105 °.

Answer: The angles of the quadrilateral are 75 °, 85 °, 95 ° and 105 °.