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Using a protractor, draw an angle of measure $72^o$. With this angle as given, draw angles of measure $36^o$ and $54^o$.
To do:
We have to draw an angle of measure $72^o$ using a protractor and with this angle as given we have to draw angles of measure $36^o$ and $54^o$.
Solution:
Steps of construction:
(i) Draw an angle $ABC = 72^o$ with the help of a protractor.
(ii) With centre $B$ and a suitable radius, draw an arc $EF$.
(iii) With centre $E$ and $F$ draw arcs intersecting each other at $G$ and produce it to $D$.
This implies,
$BD$ is the bisector of $\angle ABC$.
Therefore,
$\angle DBC = \frac{1}{2}\times72^o$
$= 36^o$
(iv) Bisect $\angle ABD$ in the same way then $PB$ is the bisector of $\angle ABD$.
Therefore,
$\angle PBC = 36^o + \frac{1}{2} \times 36^o$
$= 36^o + 18^o$
$= 54^o$
Hence, $\angle PBC = 54^o$.
Updated on: 10-Oct-2022
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