We are asked to draw an angle of 108°, using protractor and obtain an angle of 54°

We will follow certain algorithm for this construction

Steps of construction

STEP1: Using the protractor, draw angle ABC of measure 108°.

STEP2: With centre B, and taking any radius, draw an arc, intersecting the ray BA and the ray BC at point D and E respectively.

STEP 3: With centre D and radius greater than half of DE, draw an arc inside the angle.

STEP 4: With centre E and taking the same radius as in STEP 3, draw an arc intersecting the arc drawn in STEP 3, at F.

STEP 5: Draw the ray BF. This is the angle bisector of angle ABC. So angle FBC = 54°.

STEP 6: With centre B and taking any radius, draw an arc intersecting the ray BF and the ray BC at G and H respectively.

STEP 7: Draw a ray MN.

STEP 8: With centre M and taking the same radius as in STEP 6, draw an arc intersecting the ray MN at point P.

STEP 9: With centre P and taking radius equal to HG, draw an arc intersecting the arc drawn in STEP 8, at point L.

STEP 10: Draw the ray ML.

Angle LMN is the desired angle of measure 54°