We are asked to draw a linear pair of angles and bisect each of them and verify that the two bisecting rays are perpendicular to each other

We follow the following algorithm for construct

Steps of construction

STEP1: Draw a linear pair of angles and label them as ABD and DBC.

STEP2: Draw an arc of sufficient radius, intersecting the ray BA, ray BD and the ray BC at points G, H and I respectively.

STEP3: With centre I and radius greater than half of HI draw an arc inside of DBC.

STEP4: With centre G and the same radius draw an arc inside of ABD.

STEP5: With centre H and the same radius, draw two arcs one on each side of the ray BD and intersecting the arc drawn in STEP 3 at F and the arc drawn in STEP 4 at E.

STEP6: Draw the ray BE and the ray BF.

After the measurement, it can be verified that EBF is a right angle.

Hence the ray BE and the ray BF are perpendicular to each other.