Question

Using protractor, draw an angle of measure ${108}^{\circ }.$ With this angle as given, draw an angle of ${54}^{\circ }.$

Answer 1

We are asked to draw an angle of ${108}^{\circ }$, using protractor and obtain an angle of ${54}^{\circ }$.

We will follow certain algorithm for this construction:

Steps of construction:

STEP1: Using the protractor, draw angle $ABC$ of measure ${108}^{\circ }$.

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 $FBC={54}^{\circ }$.

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 ${54}^{\circ }$