Chapter 8.5, Problem 51E

(a)

To determine

To construct: An acute angle from the given numbers.

Explanation of Solution

Given information: The given coordinates of the ray is $\left(4,0\right)$ and the numbers are $\begin{array}{ccccc}-2& -1& 0& 1& 2\end{array}$ .

Construction: The angle which is less than $90°$ in measure is known as acute angle.

For construction of an acute angle, following method should be followed.

Plot the ray from origin through $\left(4,0\right)$ .

We can say that a point should be lying in the first quadrant.

The possible point will be at $\left(2,1\right)$

  

(b)

To determine

To construct: A right angle from the given numbers.

Explanation of Solution

Given information: The given coordinates of the ray is $\left(4,0\right)$ and the numbers are $\begin{array}{ccccc}-2& -1& 0& 1& 2\end{array}$ .

Construction: The angle which is equal to $90°$ in measure is known as right angle.

For construction of the right angle, following method should be followed.

• Plot the ray from origin through $\left(4,0\right)$ .
• As right angles measure equal to $90°$ , so, we can say that point is going upwards along the y-axis.
• The possible point will be at $\left(0,2\right)$

  

(c)

To determine

To construct: An obtuse angle from the given numbers.

Explanation of Solution

Given information: The given coordinates of the ray is $\left(4,0\right)$ and the numbers are $\begin{array}{ccccc}-2& -1& 0& 1& 2\end{array}$ .

Construction: The angle which is less than $180°$ but greater than $90°$ in measure is known as obtuse angle.

For construction of the obtuse angle, following method should be followed.

• Plot the ray from origin through $\left(4,0\right)$ .
• As obtuse angles measure less than $180°$ but greater than $90°$ , so, we can say that point is lying in the second quadrant.
• The possible point will be at $\left(-2,1\right)$ .

  

(d)

To determine

To construct: A straight angle from the given numbers.

Explanation of Solution

Given information: The given coordinates of the ray is $\left(4,0\right)$ and the numbers are $\begin{array}{ccccc}-2& -1& 0& 1& 2\end{array}$ .

Construction: The angle which is equal to $180°$ in measure is known as straight angle.

For construction of the straight angle, following method should be followed.

• Plot the ray from origin through $\left(4,0\right)$ .
• As straight angles measure equal to $180°$ , so, we can say that point is lying along the left x-axis.
• The possible point will be at $\left(-2,0\right)$ .