The circle centered at point O is divided into four angles with different degree measures. The degree measure

The circle centered at point O is divided into four angles with different degree measures. The degree measure of the first angle a, second angle b, third angle c, fourth d. Sum of angles: first and second 140 degrees first and third 160 first and fourth 180 Find the degree measure of EACH angle.

Let us write expressions for the degree measure of angles according to the problem data:

a + b = 140º;

a + c = 160º;

a + d = 180º.

The sum of all the angles into which the circle is divided is 360º, that is:

a + b + c + d = 360º.

Let us express the degree measures of all angles through “a”:

b = 140º – a;

c = 160º – a;

d = 180º – a.

Substitute these expressions for the angles into the expression a + b + c + d = 360º and solve the equation:

a + (140 – a) + (160 – a) + (180 – a) = 360;

a + 140 – a + 160 – a + 180 – a = 360;

-2a + 480 = 360;

2a = 120;

a = 60º.

Find the rest of the corners:

b = 140 – 60 = 80º;

c = 160º – 60 = 100º;

d = 180º – 60 = 120º.