Answer:
2)
Step-by-step explanation:
1. obtuse angle is shown, 45° is missing.
2. obtuse angle is shown, 29° is missing.
3. acute angle is shown, 65° is missing.
4. acute angle is shown, 40° is missing.
5. acute angle is shown, 42° is missing.
6. acute angle is shown, 100° is missing.
7 an obtuse angle and a acute angle are shown, 54° (for number 1) and 126° (for number 2) are missing.
8. an obtuse and a acute angle are shown, 45° (for 1) and 135° (for 2) are missing.
For this case we use the following formula
Area of Sector = Area * radians of sector / 2 * pi radians
Where,
Area: it is the area of the complete circle.
We have then:
Area = pi * r ^ 2
Area = pi * (6) ^ 2
Area = 36pi
Substituting values:
5pi = 36pi * radians of sector / 2 * pi
Clearing:
radians of sector = ((5pi) * (2pi)) / (36pi)
radians of sector = (10pi ^ 2) / (36pi)
radians of sector = (10pi) / (36)
radians of sector = (10/36) pi
radians of sector = (5/18) pi
in degrees:
(5/18) pi * (180 / pi) = 50 degrees
Answer:
The measure of the central angle is:
50 degrees
