Question

If the clock is showing 3 o' clock , what angle is it making?

• A. ${90}^{\circ }$
• B. ${120}^{\circ }$
• C. ${60}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

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

$\text{3 o' clock determines the first quarter}$ $\text{of the circle.}$

$\text{To determine the measure of the angle}$ $\text{for first quarter of the clock, we have}$ $\text{to calculate the measure of angle for}$ $\text{one part of the circle out of 4.}$

$\text{Fraction of one part of the circle =}$ $\frac{1}{4}$

$\text{Measure of the angle in one complete}$ $\text{circle =}{360}^{\circ }$

$\text{We have to convert}\frac{1}{4}\text{part of the}$ $\text{circle into degrees.}$

$\text{Let's multiply the fraction}\frac{1}{4}\text{by}$ $\text{90 to make an equivalent fraction}$ $\text{with the denominator as 360.}$

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

$\text{Hence, 3 o' clock of the clock is at}$ ${90}^{\circ }\text{.}$