Joel and Melinda provide the following proofs for vertical angles to be equal:
2 answers:
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Answer:
11. A)45°
12. A)45°
13. A)45°
14. B)180°
15. C)65°
16.D)135°
17. A)115°
18. B)180°
Step-by-step explanation:
An arc measure is defined as the measure of an angle an arc creates in a circle's center.
11.#from properties of a circle, we know arcs of a circle are proportional to their corresponding angle
Hence, the arc measure DC is 45°
12.#from properties of a circle, we know arcs of a circle are proportional to their corresponding angle
Let x be the center of the circle;
Hence, the arc measure AB is 45°
13. Given BE is a diameter, we know from properties of a circle that the angle subtending it is equal to 180°.
Also, given AD is a diameter:
Hence, the arc measure ED is 45°
14.Given AD is a diameter, we know from properties of a circle that the angle subtending it is equal to 180°.
Hence, the arc measure ABD is 180°
15. Given AD is a diameter, we know from properties of a circle that the angle subtending it is equal to 180°.
Hence, the arc measure BC is 65°
16. #from properties of a circle, we know arcs of a circle are proportional to their corresponding angle:
Hence, the arc measure BD is 135°
17. From a3 above, we know the arc measure ED is 45°. The arc measure of CED is equivalent to ED plus CD:
Hence, the arc measure CED is 115°
18.Given AD is a diameter, we know from properties of a circle that the angle subtending it is equal to 180°.
Hence, the arc measure ADB is 180°