Question

11-18 please help with work shown I’m lost completely

Answer 1

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

$\angle DXB=arc \ DC\\\\45\textdegree=arc \ DC$

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;

$\angle AXB=arc \ AB\\\\45\textdegree=arc \ AB$

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°.

$\angle BXE=\angle BXA+\angle AXE=180\textdegree\\\\\angle AXE=180\textdegree-45\textdegree\\\\=135\textdegree$

Also, given AD is a diameter:

$\angle AXD=\angle EXD+\angle AXE=180\textdegree\\\\\angle EXD=180\textdegree-135\textdegree\\\\=45\textdegree$

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°.

$\angle AXD=\angle AXB+\angle BXC+\angle CXD=180\textdegree\\\\\angle BXC=180\textdegree-45\textdegree-70\textdegree\\\\=65\textdegree$

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:

$\angle BXD=\angle BXC+\angle CXD=\\\\\angle BXD=70\textdegree+65\textdegree\\\\=135\textdegree$

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:

$\angle CED=\angle DXE+\angle CXD=\\\\\angle BXD=70\textdegree+45\textdegree\\\\=115\textdegree$

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°