Question

Three friends distributed their total property. The ratio of total property, share of first friend and share of second friend is $24:7:8$. Find the central angle of sector which represents the share of the third friend.

• A. $72\frac{1^{\circ }}{2}$
• B. ${135}^{\circ }$
• C. ${105}^{\circ }$
• D. $67\frac{1^{\circ }}{2}$

Answer 1

The correct option is B ${135}^{\circ }$

Let the total property be $24x$
Share of the first friend $=7x$
Share of the second friend$=8x$
$\therefore$ share of the third friend $=24x-(7x+8x)=9x$
Angle representing the total property
$24x={360}^{\circ }$
$\therefore x=\frac{360}{24}=15$
$\therefore$ central angle which represent the share of the third friend $=9\times 15={135}^{\circ }$