Question

Find the measure of angle of the shaded region.

• A. ${72}^{\circ }$
• B. ${96}^{\circ }$
• C. ${144}^{\circ }$
• D. ${196}^{\circ }$

Answer 1

The correct option is C ${144}^{\circ }$

$\text{The circle is divided into 5 equal}$ $\text{parts, out of which 2 parts are shaded}$ $\text{in green color.}$

$\text{To determine the measure of the angle}$ $\text{for shaded region of the circle, we have}$ $\text{to calculate the measure of angle for}$ $\text{one part of the circle.}$

$\text{Fraction of one part of the circle =}$ $\frac{1}{5}$

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

$\text{We have to convert}\frac{1}{5}\text{part of the}$ $\text{circle into degrees.}$

$\text{Let's multiply the fraction}\frac{1}{5}\text{by}$ $\text{72 to make an equivalent fraction}$ $\text{with the denominator as 360.}$

$⟹$ $\frac{1\times 72}{5\times 72}=$ $\frac{72}{360}$

$\text{Hence, each part of a circle measures}$ $\text{as}{72}^{\circ }\text{.}$

$\text{To determine the total angle of the}$ $\text{shaded region, let's}$ $\text{multiply 72 by 2.}$

$⟹2\times {72}^{\circ }={144}^{\circ }$

$\text{Hence, the total angle for the shaded}$ $\text{region is}{144}^{\circ }\text{.}$