Question

Ray OE moves $\frac{1}{4}$ part of a circle to find a new position on the circle. What will be the measure of the angle, so formed?

• A. ${90}^{\circ }$
• B. ${45}^{\circ }$
• C. ${180}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is A ${90}^{\circ }$

$\text{One part measures}\frac{1}{4}\text{of the circle.}$

$\text{For finding the angle subtended by}$ $\frac{1}{4}\text{part of the circle, we need to}$ $\text{convert the fraction into an equivalent}$ $\text{fraction with the denominator as 360.}$

$⟹$ $\frac{1\times 90}{4\times 90}=$ $\frac{90}{360}$


$\text{As we know, measure of the angle}$ $\text{that occupies}\frac{90}{360}\text{part of the circle is}$ $\text{1 degree.}$

$\frac{1}{360}$ $\text{part of a circle =}$ $1^{\circ }$

$\frac{90}{360}$ $\text{part of a circle =}$ ${90}^{\circ }$

As one part of a circle measures 1 degree of an angle, 90 parts of the circle measure 90 degrees of the circle. So, the measure of the angle is 90 degrees.