Question

Using your protractor, draw an angle of measure 108°. With this angle as given, draw an angle of 54°.

Answer 1

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 ∠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 D and E as centre and radius greater than half of DE, draw arcs to intersect each other at say F.

STEP 4: Draw the ray BF. This is the angle bisector of ∠ABC. So ∠FBC = 54°.

STEP 5: With centre B and taking any radius, draw an arc intersecting the ray BF and the ray BC at G and H respectively.

STEP 6: Draw a ray MN.

STEP 7: With centre M and taking the same radius as in STEP 5, draw an arc intersecting the ray MN at point P.

STEP 8: With centre P and taking radius equal to HG, draw an arc intersecting the arc drawn in STEP 7, at point L.

STEP 9: Draw the ray ML.

∠LMN is the desired angle of measure 54°.