Chapter 57, Problem 13A

To determine

(a)

Construct the angle $45°$ and check by using protractor.

Explanation of Solution

Given:

An angle is $45°$.

Construction:

Following are the steps of construction for angle $45°$:

• Draw a horizontal line segment named as OB.
• Take a point O and make a semicircular arc on the line with the help of compass.
• Cut the semicircular arc two times and name as point D and C.
• Make an angular bisector from points D and C.
• Draw a line of $90°$ from O.
• Bisect the $90°$ to get $45°$ .

The angle $45°$ is shown below:

Check the angle by applying a protector on the line OB as follows:

To determine

(b)

Construct the angle $22°30^{\prime }$ and check by using protractor.

Explanation of Solution

Given:

An angle is $22°30^{\prime }$.

Construction:

Following are the steps of construction for angle $22°30^{\prime }$:

• Draw a horizontal line segment named as OA.
• Take a point O and make a semicircular arc on the line with the help of compass.
• Cut the semicircular arc two times.
• Make an angular bisector from two points.
• Draw a line of $90°$ from O.
• Bisect the $90°$ to get $45°$ .
• Again, bisect the angle $45°$ to get $22°30^{\prime }$.

The angle $22°30^{\prime }\text{or}22.5°$ is shown below:

Check the angle by applying a protector on the line OB as follows:

To determine

(c)

Construct the angle $67°30^{\prime }$ and check by using protractor.

Explanation of Solution

Given:

An angle is $67°30^{\prime }$.

Construction:

Following are the steps of construction for angle $67°30^{\prime }$:

• Draw a horizontal line segment named as OA.
• Take a point O and make a semicircular arc on the line with the help of compass.
• Cut the semicircular arc two times.
• Make an angular bisector from two points.
• Draw a line of $90°$ from O.
• Bisect the $90°$ to get $45°$ .
• Again, bisect the angle formed between $45°$ and $90°$ to get $67°30^{\prime }$.

The angle $22°30^{\prime }\text{or}22.5°$ is shown below:

Check the angle by applying a protector on the line OB as follows:

To determine

(d)

Construct the angle $157{\frac{1}{2}}^{°}$ and check by using protractor.

Explanation of Solution

Given:

An angle is $157{\frac{1}{2}}^{°}$.

Construction:

Following are the steps of construction for angle $157{\frac{1}{2}}^{°}$:

• Draw a horizontal line segment named as OB.
• Take a point O and make a semicircular arc on the line with the help of compass.
• Cut the semicircular arc two times.
• Make an angular bisector from two points.
• Draw a line of $90°$ from O.
• Bisect the angle formed between $90°$ and $180°$ to get $135°$ .
• Again, bisect the angle formed between $135°$ and $180°$ to get $157.5°$.

The angle $157.5°$ is shown below:

Check the angle by applying a protector on the line OB as follows:

To determine

(e)

Construct the angle $168{\frac{3}{4}}^{°}$ and check by using protractor.

Explanation of Solution

Given:

An angle is $168{\frac{3}{4}}^{°}$.

Construction:

Following are the steps of construction for angle $168{\frac{3}{4}}^{°}$:

• Draw a horizontal line segment named as OB.
• Take a point O and make a semicircular arc on the line with the help of compass.
• Cut the semicircular arc two times.
• Make an angular bisector from two points.
• Draw a line of $90°$ from O.
• Bisect the angle formed between $90°$ and $180°$ to get $135°$ .
• Bisect the angle formed between $135°$ and $180°$ to get $157.5°$.
• Again, bisect the angle formed between $157.5°$ and $180°$ to get $168.75°$.

The angle $168.75°$ is shown below:

Check the angle by applying a protector on the line OB as follows: