Find adjacent angles if: 1) one of them is 30 degrees larger than the other;

Find adjacent angles if: 1) one of them is 30 degrees larger than the other; 2) their difference is 40 degrees; 3) one of them is 3 times smaller than the other; 4) they are equal

The sum of adjacent angles is 180 degrees.

1) Let one angle be x, then the second angle is (x + 30). The sum of the angles is (x + (x + 30)) degrees or 180 degrees.

x + (x + 30) = 180;

x + x + 30 = 180;

2x + 30 = 180;

2x = 180 – 30;

2x = 150;

x = 150: 2;

x = 75;

x + 30 = 75 + 30 = 105.

Answer. 75; 105.

2) If the difference between the two angles is 40 degrees, this means that one angle is 40 degrees larger than the other.

Let one angle be x, then the second angle is (x + 40). The sum of the angles is (x + (x + 40)) degrees or 180 degrees.

x + (x + 40) = 180;

x + x + 40 = 180;

2x + 40 = 180;

2x = 180 – 40;

2x = 140;

x = 140: 2;

x = 70;

x + 30 = 70 + 40 = 110.

Answer. 70; 110.

3) Let one angle be x degrees, then the second angle is 3x degrees. The sum of the angles is (x + 3x) degrees or 180 degrees.

x + + 3x = 180;

4x = 180;

x = 180: 4;

x = 45;

3x = 45 * 3 = 135.

Answer. 45; 135.

4) If the angles are the same, and their sum is 180 degrees, then to find these angles you need to divide 180 in half.

180: 2 = 90

Answer. 90; 90.