Question

What is the approximate measure of this angle in degrees?

(a) \[{{20}^{\circ }}\]
(b) \[{{45}^{\circ }}\]
(c) \[{{110}^{\circ }}\]
(d) \[{{135}^{\circ }}\]

Answer 1

Hint: First understand the basic types of angles and their definitions. Try to eliminate the options one – by – one by using the definitions of different types of angles. Also, check for the inclination of the ray towards the base line to differentiate between acute angles.

Complete step by step answer:
We have to find the approximate measure of the angle shown in the figure.

First let us see what are different types of angles.
1. Acute angle: -
Acute angles are angles which lie between \[{{0}^{\circ }}\] and \[{{90}^{\circ }}\].

2. Right angle: -
An angle whose measure is \[{{90}^{\circ }}\] is called a right angle.

3. Obtuse angle: -
Angle whose range is from \[{{90}^{\circ }}\] to \[{{180}^{\circ }}\] is called an obtuse angle.

4. Straight angle: -
An angle whose measure is \[{{180}^{\circ }}\] is called a straight angle.

Now, after reading the above definitions of different angles we get that, \[{{110}^{\circ }}\] and \[{{135}^{\circ }}\] are obtuse angles and \[{{20}^{\circ }}\] and \[{{45}^{\circ }}\] are acute angles. It is clear that \[{{110}^{\circ }}\] and \[{{135}^{\circ }}\] cannot be our answer because the figure given in question is same as the figure used for representations of acute angles. So, options (c) and (d) are eliminated.
Now, we have two angles \[{{20}^{\circ }}\] and \[{{45}^{\circ }}\] left with us. We know that the more is the inclination of a ray towards baseline the less is the angle. So, on observing the figure carefully we can see that the ray is not inclined too much towards the base line. Therefore, \[{{20}^{\circ }}\] cannot be our answer. So, \[{{45}^{\circ }}\] is the correct answer.
So, the correct answer is “Option B”.

Note: One may note that we have used the method of elimination of options to get the correct answer. This method is pretty useful when we have some less information given in the question. It was clear to us that the given angle is an acute angle but is not possible to determine the angle if options are not given and we do not have a protractor.