2. find the fraction piece that would cover half the circle. trace the fraction on the circle. label your circle as shown.

4. how much of the circle would have a measure of 90 degrees? how would you write 90 degrees as a fraction of your circle?

5. find the fraction pieces that would make 90 - degree angles. label your circle as shown.

6. use the benchmarks of 90 and 180 degrees to find the angles with measures of 45 degrees, 60 degrees, and 120 degrees. label them on the circle.

7. fold the circle in half. on the blank side, repeat steps 2 - 4 labelling 180 degrees on the opposite side than its label on the completed protractor.

Question

2. find the fraction piece that would cover half the circle. trace the fraction on the circle. label your circle as shown.

4. how much of the circle would have a measure of 90 degrees? how would you write 90 degrees as a fraction of your circle?

5. find the fraction pieces that would make 90 - degree angles. label your circle as shown.

6. use the benchmarks of 90 and 180 degrees to find the angles with measures of 45 degrees, 60 degrees, and 120 degrees. label them on the circle.

7. fold the circle in half. on the blank side, repeat steps 2 - 4 labelling 180 degrees on the opposite side than its label on the completed protractor.

Accepted Answer

### Question 4:
# Explanation:
## Step1: Recall the total degrees in a circle
A full circle has $ 360^\circ $.
## Step2: Calculate the fraction for $ 90^\circ $
To find the fraction of the circle that $ 90^\circ $ represents, we divide $ 90^\circ $ by $ 360^\circ $. So the fraction is $ \frac{90}{360} $.
## Step3: Simplify the fraction
Simplify $ \frac{90}{360} $ by dividing both the numerator and the denominator by their greatest common divisor, which is 90. $ \frac{90\div90}{360\div90}=\frac{1}{4} $.
# Answer:
The measure of $ 90^\circ $ is $ \frac{1}{4} $ of the circle.

### Question 5:
# Explanation:
## Step1: Recall the fraction for $ 90^\circ $
From question 4, we know that $ 90^\circ $ is $ \frac{1}{4} $ of a full circle ($ 360^\circ $).
## Step2: Determine the fraction pieces
To make $ 90^\circ $ angles, we need to divide the circle into parts where each part is $ \frac{1}{4} $ of the circle (since $ 90^\circ=\frac{1}{4}\times360^\circ $). So the fraction pieces are $ \frac{1}{4} $ of the circle. When we divide the circle into 4 equal parts (by drawing two perpendicular diameters, like a plus sign in the circle), each part will have a central angle of $ 90^\circ $.
# Answer:
The fraction pieces that make $ 90^\circ $ angles are $ \frac{1}{4} $ of the circle. We can label the circle by drawing two perpendicular lines through the center, dividing the circle into 4 equal - sized sectors, each with a central angle of $ 90^\circ $.

### Question 6:
# Explanation:
## Step1: Analyze $ 45^\circ $
We know that $ 90^\circ $ is a benchmark. $ 45^\circ $ is half of $ 90^\circ $. So to find $ 45^\circ $, we can bisect a $ 90^\circ $ angle. If we have a $ 90^\circ $ sector (from question 4 or 5), we can divide it into two equal parts, and each part will be $ 45^\circ $.
## Step2: Analyze $ 60^\circ $
We know that a full circle is $ 360^\circ $, and an equilateral triangle has internal angles of $ 60^\circ $. Also, we can use the relationship with $ 90^\circ $ and $ 180^\circ $. Since $ 180^\circ $ is a straight angle (half of the circle), and $ 60^\circ=\frac{1}{3}\times180^\circ $. So we can divide the semicircle ($ 180^\circ $) into 3 equal parts, each part will be $ 60^\circ $.
## Step3: Analyze $ 120^\circ $
$ 120^\circ = 180^\circ - 60^\circ $, or $ 120^\circ=\frac{2}{3}\times180^\circ $. We can also think of it as $ 90^\circ+ 30^\circ $, but more simply, since $ 120^\circ=\frac{1}{3}\times360^\circ $ (because $ 360\div3 = 120 $) or as $ 180 - 60 $. To label $ 120^\circ $, we can find a $ 60^\circ $ angle and then the supplementary angle to it (with respect to $ 180^\circ $) will be $ 120^\circ $, or we can divide the circle into 3 equal parts (each $ 120^\circ $) or use the $ 90^\circ $ and $ 30^\circ $ (but $ 30^\circ $ can be derived from $ 90^\circ\div3 $) to build up $ 120^\circ=90 + 30 $.
# Answer:
- $ 45^\circ $: Bisect a $ 90^\circ $ angle (for example, the $ 90^\circ $ sector from the previous questions). The angle formed by the bisector and one of the sides of the $ 90^\circ $ angle is $ 45^\circ $.
- $ 60^\circ $: Divide the semicircle ($ 180^\circ $) into 3 equal parts. Each part will have a central angle of $ 60^\circ $.
- $ 120^\circ $: We can either find the supplementary angle of $ 60^\circ $ (since $ 180 - 60=120 $) or divide the full circle into 3 equal parts (each part is $ 120^\circ $) or add a $ 30^\circ $ angle to a $ 90^\circ $ angle (where $ 30^\circ $ is $ \frac{1}{3}$ of $ 90^\circ $). Label these angles on the circle by marking the appropriate positions based on these constructions.

### Question 7:
# Explanation:
## Step1: Fold the circle in half
Folding the circle in half will create a semicircle, and the crease will be a diameter of the circle, corresponding to a $ 180^\circ $ angle (as a semicircle has an arc measure of $ 180^\circ $).
## Step2: Repeat steps 2 - 4 on the blank side
- Step 2 (similar to original step 2): Find the fraction piece that covers half the circle. Since we folded the circle in half, the fraction is $ \frac{1}{2} $ (as a semicircle is half of a full circle, $ 180^\circ=\frac{1}{2}\times360^\circ $).
- Step 3 (similar to original step 3): Find the fraction piece for $ 90^\circ $. On the semicircle ($ 180^\circ $), a $ 90^\circ $ angle is half of the semicircle. So the fraction is $ \frac{90}{180}=\frac{1}{2} $ of the semicircle or $ \frac{1}{4} $ of the full circle (same as before, since $ 90^\circ=\frac{1}{4}\times360^\circ $). We can label the $ 180^\circ $ on the opposite side of its original label by marking the diameter (crease) as the $ 180^\circ $ angle on the blank side, and then mark the $ 90^\circ $ angles by bisecting the semicircle (drawing a line perpendicular to the diameter at the center, creating two $ 90^\circ $ angles on the blank side).
# Answer:
When we fold the circle in half, we get a semicircle. On the blank side, for step 2 (finding the fraction piece that covers half the circle), the fraction is $ \frac{1}{2} $ (since the folded circle (semicircle) is half of the full circle). For step 3 (finding the fraction piece for $ 90^\circ $), on the semicircle ($ 180^\circ $), $ 90^\circ $ is $ \frac{1}{2} $ of the semicircle (or $ \frac{1}{4} $ of the full circle). For step 4 (labeling), we label $ 180^\circ $ on the opposite side (the crease from folding is the $ 180^\circ $ angle on the blank side) and label the $ 90^\circ $ angles by bisecting the semicircle (drawing a perpendicular to the diameter at the center) to get two $ 90^\circ $ angles on the blank side.

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QUESTION IMAGE

Question

Explanation:

Question 4:

Step1: Recall the total degrees in a circle

Step2: Calculate the fraction for \( 90^\circ \)

Step3: Simplify the fraction

Step1: Recall the fraction for \( 90^\circ \)

Step2: Determine the fraction pieces

Step1: Analyze \( 45^\circ \)

Step2: Analyze \( 60^\circ \)

Step3: Analyze \( 120^\circ \)

Answer:

Question 5: