Chapter 1, Problem 15CR

To determine

To state : whether the given angle is acute or obtuse.

Answer to Problem 15CR

The given angle $\angle CBD$ is an obtuse angle.

Explanation of Solution

Given information : The given angle is $\angle CBD$ and a figure shown below

An angle is said to be acute if its measure is less than ${90}^{°}$ and obtuse whose measure is greater than ${90}^{°}$

Here $\angle ABC$ is a straight angle whose measure is ${180}^{°}$ .

Now,

  $\begin{array}{c}\angle ABD+\angle DBC=\angle ABC\\ {88}^{°}+\angle DBC={180}^{°}\\ \angle DBC={180}^{°}-{88}^{°}\\ ={92}^{°}\end{array}$

Therefore, we get $\angle CBD$ is an obtuse angle.