Question

Draw an angle of ${110}^{\circ }$ with the help of a protractor and bisect it. Measure each angle.

Answer 1

Draw an angle of ${110}^{\circ }$ with the help of a protractor. Now, we use the following steps for required construction.

(i) Taking X as the centre and any radius, draw an arc to intersect the rays XA and XB, say at E and D, respectively.
(ii) Taking D and E as the centres and with the radius more than $\frac{1}{2}$ DE, draw arcs to intersect each other, say at F.
(iii) Draw the ray XC which passes through the point F.
Thus, ray XF is the required bisector of the $\angle BXA$.

On measuring each angle, we get
$\angle BXC=\angle AXC={55}^{\circ }$
$[\because \angle BXC=\angle AXC=\frac{1}{2}\angle BXA=\frac{1}{2}\times {110}^{\circ }={55}^{\circ }]$