Question

Matt cut a circle into 8 equal sections. He drew an angle that measures the same as the total measure of 4 of the sections in the circle. What is the measure of the angle Matt drew?

Answer 1

The angle Matt drew = 180°

Explanation:

The total angle formed by the 8 angles Matt drew in the circle equals 360° because one revolution of a circle is the same as the angle about a point which equals 360°.

Let the equal angles drawn = x

x + x + x + x + x + x + x + x = 360°

8 × x = 360°

8x = 360

x = 45°

∴ each angle drawn = 45°

Next, we are told that Matt drew another angle that has the same measurement as four (4) of the sections (angles) in the circle.

Finding the measure of this angle:

1 section in the circle = 45 (shown above)

∴ 4 sections = 45 × 4 = 180°

∴ The angle Matt drew = 180°