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

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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\$.

Updated on 10-Oct-2022 13:41:45