Question

There are seven equal chords in the circle with centre O in the given figure. The value of x will be ?

• A. $(128\frac{4}{7}{)}^{\circ }$
• B. $(180\frac{6}{7}{)}^{\circ }$
• C. $(128\frac{1}{7}{)}^{\circ }$
• D. $(360\frac{4}{7}{)}^{\circ }$

Answer 1

The correct option is A $(128\frac{4}{7}{)}^{\circ }$

Join OA , OB and OC. There are seven equal chords and each chord makes equal central angle at the centre




Hence, $\angle AOB=\frac{{360}^{\circ }}{7}$
$\therefore \angle AOC=2\times \frac{{360}^{\circ }}{7}=\frac{{720}^{\circ }}{7}$
$\therefore reflex\angle AOC={360}^{\circ }-\frac{{720}^{\circ }}{7}={360}^{\circ }(1-\frac{2}{7})={360}^{\circ }\times \frac{5}{7}$
$(1-\frac{2}{7})={360}^{\circ }\times \frac{5}{7}$
$\because$ Angle at the centre is twice the angle at circumference.
$\therefore {360}^{\circ }\times \frac{5}{7}=2x\Rightarrow x=\frac{{360}^{\circ }\times 5}{2\times 7}$
$=\frac{{900}^{\circ }}{7}=(128\frac{4}{7}{)}^{\circ }$