Question

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

• A. $250°$
• B. $125°$
• C. $280°$
• D. $225°$

Answer 1

The correct option is D $225°$

The compass has 8 directions. We need to calculate the measure of the angle between north and south-west.
● Each direction on the compass covers $\frac{1}{8}$ 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 5 divisions from north to south-west on the compass.
● The measure of the angle between north and south-west $=5\times 45°=225°$

Hence, D is the correct option.