Question

Ray $OB$ moves $\frac{1}{8}$ part of a circle to find a new position $O{B}^{\prime }$ on the wheel. What will be the measure of angle $BO{B}^{\prime }$?

• A. ${50}^o$
• B. ${20}^o$
• C. ${45}^o$
• D. ${35}^o$

Answer 1

The correct option is C ${45}^o$

Ray $OB$ moves $\frac{1}{8}$ part of a circle to a new position $O{B}^{\prime }$.

● Write $\frac{1}{8}$ as an equivalent fraction with \$360$ as the denominator.

$=\frac{1}{8}=\frac{1\times 45}{8\times 45}=\frac{45}{360}$

● Write $\frac{45}{360}$ parts of the circle in degrees.

$\frac{45}{360}$ parts of a circle $={45}^o$

● So, $OB$ moved $45°$ to a new position $O{B}^{\prime }$.


Hence, D is the correct option.