Question
Draw an angle of $65^\circ$ and draw an angle equal to this angle, using ruler and compasses.
✓
Answer
Given, $\angle\text{B}=65^\circ$
Step of construction are as follows:
Step I: Draw a line $l$ and choose a point $P$ on it.
Step II: Place the compass at $B$ and draw an arc to cut the rays of $\angle\text{B}$ at $A$ and $C.$
Step III: Use the same compass setting to draw an arc with $P$ as centre, cutting $l$ at $Q.$
Step IV: Set your compass to the length $AC.$
Step V: Place the compass pointer at $Q$ and draw the arc to cut the previous arc in $R.$
Step VI: Join $PR.$ This gives us $\angle \text{P}.$ It has the same measure as $\angle\text{B.}$
This means $\angle\text{QPR}$ has same measure as $\angle\text{ABC.}$
Step of construction are as follows:
Step I: Draw a line $l$ and choose a point $P$ on it.
Step II: Place the compass at $B$ and draw an arc to cut the rays of $\angle\text{B}$ at $A$ and $C.$
Step III: Use the same compass setting to draw an arc with $P$ as centre, cutting $l$ at $Q.$
Step IV: Set your compass to the length $AC.$
Step V: Place the compass pointer at $Q$ and draw the arc to cut the previous arc in $R.$
Step VI: Join $PR.$ This gives us $\angle \text{P}.$ It has the same measure as $\angle\text{B.}$
This means $\angle\text{QPR}$ has same measure as $\angle\text{ABC.}$
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