Find adjacent angles if: 1) one of them is 70 degrees larger than the second;

Find adjacent angles if: 1) one of them is 70 degrees larger than the second; 2) one of them is 8 times smaller than the second. 3) their degree measures are related as 3: 2.

Adjacent corners are corners, one side of which is common, and the other two are complementary half-lines. The sum of the degree measures of adjacent angles is 180 °.

1) Since the angle ∠1 is 70 ° more than the angle ∠2, and their sum is 180 °, we express it like this:

x is the degree measure of the angle ∠2;

x + 70 – degree measure of angle ∠1;

x + x + 70 = 180;

x + x = 180 – 70;

2x = 110;

x = 110/2 = 55;

∠2 = 55 °;

∠1 = 55 ° + 70 ° = 125 °.

2) Since ∠1 is eight times less than the angle ∠2, then:

x is the degree measure of the angle ∠1;

8x – degree measure of angle ∠2;

x + 8x = 180;

9x = 180;

x = 180/9 = 20;

∠1 = 20 °;

∠2 = 8 20 = 160 °.

3) Since the degree measures of these angles are related as 3: 2, then:

3x – degree measure ∠1;

2x – degree measure of angle ∠2;

3x + 2x = 180;

5x = 180;

x = 180/5 = 36;

∠1 = 3 36 = 108 °;

∠2 = 2 36 = 72 °.