Find adjacent angles if: 1. Their difference is 50 ° 2. One of them is 4 times larger than the other 3

Find adjacent angles if: 1. Their difference is 50 ° 2. One of them is 4 times larger than the other 3. Their degree measures are related as 3/7.

Adjacent angles are angles that add up to a flat angle (180 °). They have one side in common, and the other two are additional straight lines.

1) Since the sum of the degree measures of these angles is 180 °, and their difference is 50 °, we express:

x – degree measure of angle ∠1;

x + 50 – degree measure of angle ∠2;

x + x + 50 = 180;

2x = 180 – 50 = 130;

x = 130/2 = 65;

∠1 = 65 °;

∠2 = 65 + 50 = 115 °.

2) Since one of the corners is 4 times larger than the other:

x – degree measure ∠1;

4x – degree measure ∠2;

x + 4x = 180;

5x = 180;

x = 180/5 = 36;

∠1 = 36 °;

∠2 = 36 4 = 144 °.

3) Since the degree measures of these angles are related as 3: 7:

3x – degree measure ∠1;

7x – degree measure ∠2;

3x + 7x = 180;

10x = 180;

x = 180/10 = 18;

∠1 = 3 18 = 54 °;

∠2 = 7 18 = 126 °.