Question

What is the measure of the angle between north and south?

• A. $120°$
• B. $140°$
• C. $150°$
• D. $180°$

Answer 1

The correct option is D $180°$

The compass has 8 directions. We need to calculate the measure of the angle between north and south.
● Each division subtends $\frac{1}{8}$ part of a circle.
● $360°$ is the measure of the angle in one complete circle.
● $1$ degree is the measure of the angle that occupies $\frac{1}{360}$ of a circle.
● We can convert $\frac{1}{8}$ part of a circle into degrees by changing the denominator to $360$.
● $\frac{1}{8}\times \frac{45}{45}=\frac{45}{360}$
● $45°$ is the measure of the angle subtended by each division on the compass.
● There are 4 divisions from north to south on the compass.
● The measure of the angle between north and south $=4\times 45°=180°$
Hence, B is the correct option.