Question

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

Answer 1

`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`