Construct the following angles and verify by measuring them by a protractor:
(i) $ 75^{\circ} $
(ii) $ 105^{\circ} $
(iii) $ 135^{\circ} $.

To do:

We have to construct the given angles and verify them by measuring them with a protractor.

Solution:

(i)

Steps of construction:

(a) Draw a ray $BC$.

(b) With centre $B$ and a suitable radius, draw an arc meeting $BC$ at $E$.

(c) Cut off arc $EF = FG$ from $E$.

(d) Bisect the arc $FG$ at $K$ and join $BK$ so that $\angle KBC = 90^o$.

Bisect arc $HF$ at $L$ and join $BL$ and produce it to $

Therefore,

$\angle ABC = 75^o$.

(ii)

Steps of construction:

(a) Draw a ray $BC$.

(b) With centre $B$ and a suitable radius draw an arc meeting $BC$ at $E$.

(c) From $E$, cut off arc $EF = FG$ and divide $FG$ at $H$.

(d) Join $BH$ meeting the arc at $K$.

(e) Bisect the arc $KG$ at $L$.

Join $BL$ and produce it to $A$.

Therefore,

$\angle ABC = 105^o$.

(iii)

Steps of construction:

(a) Draw a ray $BC$.

(b) With centre $B$ and a suitable radius, draw an arc meeting $BC$ at $E$.

(c) From $E$, cut off $EF = FG = GH$.

(d) Bisect arc $FG$ at $K$ and join them.

(e) Bisect arc $KH$ at $L$.

(f) Join $BL$ and produce it to $A$

Therefore,

$\angle ABC = 135^o$. 

Tutorialspoint

Updated on: 10-Oct-2022

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