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
[tex]\angle DXB=arc \ DC\\\\45\textdegree=arc \ DC[/tex]
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;
[tex]\angle AXB=arc \ AB\\\\45\textdegree=arc \ AB[/tex]
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°.
[tex]\angle BXE=\angle BXA+\angle AXE=180\textdegree\\\\\angle AXE=180\textdegree-45\textdegree\\\\=135\textdegree[/tex]
Also, given AD is a diameter:
[tex]\angle AXD=\angle EXD+\angle AXE=180\textdegree\\\\\angle EXD=180\textdegree-135\textdegree\\\\=45\textdegree[/tex]
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°.
[tex]\angle AXD=\angle AXB+\angle BXC+\angle CXD=180\textdegree\\\\\angle BXC=180\textdegree-45\textdegree-70\textdegree\\\\=65\textdegree[/tex]
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:
[tex]\angle BXD=\angle BXC+\angle CXD=\\\\\angle BXD=70\textdegree+65\textdegree\\\\=135\textdegree[/tex]
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:
[tex]\angle CED=\angle DXE+\angle CXD=\\\\\angle BXD=70\textdegree+45\textdegree\\\\=115\textdegree[/tex]
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°
