We are asked to draw a pair of vertically opposite angles bisect each of them and verify that the two of them are in the sane line

We will follow the following algorithm for construction

Steps of construction

STEP1: Draw a pair of vertically opposite angles, ABC and DBE.

STEP2: With B as a centre, and taking any radius, draw an arc intersecting the ray BD and the ray BE at points F and G, respectively.

STEP3: With G as a centre, and radius greater than half of FG, draw an arc inside of DBE.

STEP4: With F as a centre, and taking the same radius as in STEP 3, draw an arc intersecting the arc drawn in STEP 3, at N.

STEP 5: Draw the ray BN.

STEP6: With B as a centre, and taking any radius, draw an arc intersecting the ray BA and the ray BC at points H and K, respectively.

STEP7: With H as a centre, and radius greater than half of HK, draw an arc inside of ABC.

STEP8: With K as a centre, and taking the same radius as in STEP 7, draw an arc intersecting the arc drawn in STEP 7, at M

STEP9: Draw the ray BM

After measuring the MBN, it can be verified that the bisecting rays BM and BN are in the same line.