Question

How many angler bisectors are drawn to construct an angle of ${22.5}^{\circ }$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

Steps to construct an angle of $22{\frac{1}{2}}^{\circ }$

1.Construct $\angle UPQ={90}^{\circ }$ by using a compass (see figure).

2. Angle bisector of ${90}^{\circ }$ angle :---(1)
With R and V as centres, draw arcs with radius more than $\frac{1}{2}RV$, to intersect each other at W and join PW.
Let the ray PW intersect the arc at X.

3. Angle bisector of ${45}^{\circ }$ angle:---(2)
Taking X and R as the centre, with a radius more than $\frac{1}{2}RX$, draw arcs to intersect each other at Y.
Joint PY which is the required ray that makes an angle of $22{\frac{1}{2}}^{\circ }$ with the ray PQ.

$\therefore$ 2 angle bisectors are drawn to construct an angle of ${22.5}^{\circ }$.