Q15. - Geometry

Question

What kind of angle is $\angle CBD$?

Step-by-Step Solution

Answer

The angle $\angle CBD$ represents itself as an obtuse angle.

Step 1. Definition of acute and obtuse angle.

The angle having the measurement below $90°$ represents itself as an acute angle but if its measurement is above $90°$ then it will represent itself as an obtuse angle.

Step 2. Observe the figure and determine the value of given angle.

In the given figure $\angle ABC$ represents itself as a straight angle so make an equation by taking the addition of the angles $\angle ABD$ and $\angle CBD$ equal to $180°$. The value of angle $\angle ABD$ is represented by $88°$.

$$\begin{gathered} m\angle CBD+m\angle ABD=180° \\ m\angle CBD+88°=180° \\ m\angle CBD=180°-88° \\ m\angle CBD=92° \end{gathered}$$

Step 3. Determine whether the given angle is an obtuse or acute angle.

The value of $\angle CBD$ is $92°$ which means that it is an obtuse angle.