Answer:
Step-by-step explanation:
1) the sum of the angles on a straight line is 180°.
Let x represent the measure of the smaller angle.
The measure of one angle is twice the measure of the other angle. This means that the larger angle is 2x. Therefore,
x + 2x = 180
3x = 180
x = 180/3 = 60
The measure of the smaller angle is 60°
The measure of the larger angle is 2 × 60 = 120°
2) The measure of one angle is 1/3 the measure of the other angle. If the measure of the larger angle is x, then the measure of the smaller angle is x/3. Therefore,
x + x/3 = 180
Multiplying through by 3, it becomes
3x + x = 180 × 3 = 540
4x = 540
x = 540/4 = 135
The smaller angle measures
135/3 = 45°
The larger angle measures 135°
3) the sum of complimentary angles is 180°
The measure of an angle is nine times the measure of its complement. If the measure of the smaller angle is x, then the measure of the larger angle is 9x. Therefore,
x + 9x = 90
10x = 90
x = 90/10 = 9
The smaller angle measures 9°
The larger angle measures 9 × 9 = 81°
4) The measure of an angle is 1/4 the measure of its complement.
If the measure of the larger angle is x, then the measure of the smaller angle is x/4. Therefore,
x/4 + x = 90
Multiplying through by 4, it becomes
x + 4x = 360
5x = 360
x = 360/5 = 72
The smaller angle measures 72/4 = 18°
The larger angle measures 72°
