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Idhi has cut out a semi-circular piece from a plastic sheet and divided it into 8 equal parts as shown: She wants to use this to measure angles. Which of the following angles will she be able to measure accurately using this semi-circular piece?​

a. 30⁰
b. 45⁰
c. 60⁰
d. 100⁰

1 Answer

3 votes

Answer:


c)\ 45^\circ

Explanation:

Given

A semicircle divided into 8 parts

Required

Angle that can be measured with the piece

First, we calculate the minimum angle that can be calculated.


\theta =(Semi\ circle)/(8)


Semicircle = 180^\circ

So, we have:


\theta =(180^\circ)/(8)


\theta =22.5^\circ

This implies that all angles that can be measured using the piece must be a multiple of 22.5 not greater than 180 degrees (i.e. not greater than the semicircle)

So, we have:


\theta =22.5^\circ,\ 45^\circ,\ 67.5^\circ,\ 90^\circ,\ 112.5^\circ,\ 135^\circ,\ 157.5^\circ,\ 180^\circ

From the list of options, only 45 degrees appear in the possible values of
\theta

Hence:


\theta = 45^\circ

User Darren Parker
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