Question
Using a protractor, draw an angle of measure 72°. With this angle as given, draw angles of measure 36° and 54°.
✓
Answer
Draw a ray OA.
With the help of a protractor, draw an angle $\angle\text{AOB}$ of 72°.
With a convenient radius and centre at O, draw an arc cutting sides OA and OB at P and Q, respectively.
With P and Q as centres and radius more than half of PQ, draw two arcs cutting each other at R.
Join O and R and extend it to X.
OR intersects arc PQ at C.
With C and Q as centres and radius more than half of CQ, draw two arcs cutting each other at T.
Join O and T and extend it to Y.
Now, OX bisects $\angle\text{AOB}$
Therefore, $\angle\text{AOX}=\angle\text{BOX}=\frac{72}{2}=36^{\circ}$
Again, OY bisects $\angle\text{BOX}$
Therefore, $\angle\text{XOY}=\angle\text{BOY}=\frac{36}{2}=18^{\circ}$
Therefore, $\angle\text{AOX}$ is the required angle of 36° and $\angle\text{AOY}=\angle\text{AOX}+\angle\text{XOY}=36^{\circ}+18^{\circ}=54^{\circ}$
Therefore, $\angle\text{AOY}$ is the required angle of 54°.
With the help of a protractor, draw an angle $\angle\text{AOB}$ of 72°.
With a convenient radius and centre at O, draw an arc cutting sides OA and OB at P and Q, respectively.
With P and Q as centres and radius more than half of PQ, draw two arcs cutting each other at R.
Join O and R and extend it to X.
OR intersects arc PQ at C.
With C and Q as centres and radius more than half of CQ, draw two arcs cutting each other at T.
Join O and T and extend it to Y.
Now, OX bisects $\angle\text{AOB}$
Therefore, $\angle\text{AOX}=\angle\text{BOX}=\frac{72}{2}=36^{\circ}$
Again, OY bisects $\angle\text{BOX}$
Therefore, $\angle\text{XOY}=\angle\text{BOY}=\frac{36}{2}=18^{\circ}$
Therefore, $\angle\text{AOX}$ is the required angle of 36° and $\angle\text{AOY}=\angle\text{AOX}+\angle\text{XOY}=36^{\circ}+18^{\circ}=54^{\circ}$
Therefore, $\angle\text{AOY}$ is the required angle of 54°.
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