Question

Construct an angle bisector to draw an angle of 45°.[3 Marks]

Answer 1

Bisecting an angle of measure ${90}^{\circ }$ (i.e. ${45}^{\circ }$ × 2) gives and angle of measure ${45}^{\circ }$.
Step 1:
Draw ∠PQR of ${90}^{\circ }$. [1 Mark]
Step 2:
Cut arcs on the rays QP and QR.
Name these points as M and N respectively. [1 Mark]

Step 3:
Place the compass point on point M and draw an arc inside the angle.
Without changing the distance of the compass, place the compass point on point N and cut the arc at O.

Step 4:
Draw ray QO.
Ray QO is the angle bisector of ∠PQR.
i.e. m∠PQO = m∠RQO = ${45}^{\circ }$ [1 Mark]