Question

An angle that is \[{{1}^{0}}\] less than right angle is:
\[\begin{align}
  & \text{(A) Reflex angle} \\
 & \text{(B) Straight angle} \\
 & \text{(C) Obtuse angle} \\
 & \text{(D) Acute angle} \\
\end{align}\]

Answer 1

Hint: We should know that if the angle \[\theta \] is greater than 0 and less than 90 is said to be an acute angle. If an angle \[\theta \] is equal to 90, then the angle is said to be the right angle. If the angle \[\theta \] is greater than 90 and less than 180 is said to be an obtuse angle. If an angle \[\theta \] is equal to 180, then the angle is said to be a straight angle. If the angle \[\theta \] is greater than 180 and less than 360 is said to be a reflex angle. If an angle \[\theta \] is equal to 360, then the angle is said to be a complete angle. Now we have to measure the angle that is \[{{1}^{0}}\] less than the right angle. Now we have to find to which category the obtained angle belongs to.

Complete step by step answer:
Before solving the question, we should know that, if the angle \[\theta \] is greater than 0 and less than 90 is said to be an acute angle. If an angle \[\theta \] is equal to 90, then the angle is said to be the right angle. If the angle \[\theta \] is greater than 90 and less than 180 is said to be an obtuse angle. If an angle \[\theta \] is equal to 180, then the angle is said to be a straight angle. If the angle \[\theta \] is greater than 180 and less than 360 is said to be a reflex angle. If an angle \[\theta \] is equal to 360, then the angle is said to be a complete angle.

From the question, it is given that an angle is \[{{1}^{0}}\] less than right angle. Let us assume the given angle as \[\theta \]. We know that the measure of an angle is equal to 90. It is given that \[\theta \] is \[{{1}^{0}}\] less than \[{{90}^{0}}\].
\[\begin{align}
  & \Rightarrow \theta ={{90}^{0}}-{{1}^{0}} \\
 & \Rightarrow \theta ={{89}^{0}} \\
\end{align}\]
As the measure of \[\theta \] is equal to \[{{89}^{0}}\]. So, it is clear that \[{{89}^{0}}\] is less than \[{{90}^{0}}\]. We know that if the angle \[\theta \] is greater than 0 and less than 90 is said to be an acute angle. So, an angle that is \[{{1}^{0}}\] less than right angle is said to be an acute angle.

So, option D is correct.

Note: This problem can be solved in an alternative way. Let us assume an angle \[\theta \]. If the ratio of \[\theta \] and 90 is less than 1, then the angle is said to be an acute angle. If the ratio of \[\theta \] and 90 is equal to 1, then the angle is said to be the right angle. If the ratio of \[\theta \] and 90 is greater than 1 and less than 2, then the angle is said to be an obtuse angle. If the ratio of \[\theta \] and 90 is equal to 2. If the ratio of \[\theta \] and 90 is greater than 2 and less than 4, then the angle is said to be reflex angle. If the ratio of \[\theta \] and 90 is equal to 4, then the angle is said to be a complete angle.
From the question, it is given that an angle is \[{{1}^{0}}\] less than right angle. Let us assume the given angle as \[\theta \]. We know that the measure of an angle is equal to 90. It is given that \[\theta \] is \[{{1}^{0}}\] less than \[{{90}^{0}}\].
\[\begin{align}
  & \Rightarrow \theta ={{90}^{0}}-{{1}^{0}} \\
 & \Rightarrow \theta ={{89}^{0}} \\
\end{align}\]
So, now let us calculate the ratio of \[\theta \] and 90.
\[\begin{align}
  & \Rightarrow \dfrac{\theta }{90}=\dfrac{89}{90} \\
 & \Rightarrow \dfrac{\theta }{90}<1 \\
\end{align}\]

As the measure of \[\theta \] is equal to \[{{89}^{0}}\]. So, it is clear that \[{{89}^{0}}\] is less than \[{{90}^{0}}\].
It is clear that the ratio of \[\theta \] and 90 is less than 1, then the angle \[\theta \] is said to be an acute angle.