How do the lengths of line segments define the golden ratio?

Step-by-step explanation:

The golden ratio is a special number favored by the Greeks. Its ratio roughly equals 1.618. The ratio is formed by taking a line segment and dividing it into two parts labeled a and b. The golden ratio is formed when this proportion is true .

When you add a and b then divide by a, it will be the same as a divided by b. This will hold true only for specific lengths of a and b. This means you must divide the line segment in such a way that a and b meet this requirement.

Example:

If the line segment is 50 cm long. Split the segment into parts a and b where a = 30.9 and b = 19.1. Substitute the values into the proportion .

1.618 = 1.618

This is the golden ratio.

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.

the answer is b.

step-by-step explanation: