Chapter 9.2, Problem 53SR

To determine

To find: The value of $\angle BMD$ .

Answer to Problem 53SR

The value of $\angle BMD$ is $140°$ and $\angle BMD$ is an obtuse angle.

Explanation of Solution

Given information:

The given figure is shown in figure (1).

  

Figure (1)

Calculation:

Angle measurement

Right angle is a geometric angle in which the measure of angle is exactly equal to $90°$ .

Acute angle is a geometric angle in which the measure of angle is less than $90°$ .

Obtuse angle is a geometric angle in which the measure of angle is more than $90°$ .

Calculate the category of the angle.

This can be done by extending the ray from point $M$ to a called point $S$ such that the ray should be straight line such that its measure should be $90°$ . This is shown in figure (2).

  

Figure (2)

It has been observed that point $D$ is going exterior or outside $\angle BMS$ which is $90°$ in measure which implies that the $\angle BMD$ is an obtuse angle as it measure will go beyond $90°$ .

Calculate the angle using protector.

Place the center of protector on $M$ and center of line $\overrightarrow{BM}$ and observing the angle of protector from beginning till the arm $\overrightarrow{MD}$ coincide. It has been observed that it is $140°$ in measure which is greater than $90°$ as expected.

  

Therefore, the value of $\angle BMD$ is $140°$ and $\angle BMD$ is an obtuse angle.