Explanation

The measure of the external angle of a regular hexagon is 60°.

This is because a hexagon has 6 sides, and the sum of the external angles of any polygon is always 360°, so 360° ÷ 6 = 60°.

Explanation

If two circles touch internally, the distance between their centers is the difference of their radii: r₁ - r₂.

r₁ is the radius of the larger circle, and r₂ is the radius of the smaller circle.

If the sum of the radii equals the distance between the centers, the circles touch externally.

Explanation

One and only one line can pass through two points.

This is because two points uniquely define a line.

Explanation

We know:

- Angle of elevation (θ) = 60°

- Distance of the foot of the ladder from the wall (x) = 12.4 m

- We need to find the length of the ladder (hypotenuse)

Using the cosine function:
cos(θ) = adjacent side / hypotenuse
cos(60°) = 12.4 / hypotenuse
To find the hypotenuse (length of the ladder), we can rearrange the equation:
hypotenuse = 12.4 / cos(60°)
Using a calculator:
hypotenuse = 12.4 / 0.5
hypotenuse = 24.8
So, the length of the ladder is 24.8 meters.

Explanation