Question

(problems 14-16 are already solved!)

14. m∠AED= 139
15. m∠CEF= 90
16. m∠DEB= 41
17. m∠BEF= ?
18. m∠CEB= ?
19. m∠ AEF= ?

Answer 1

17. 49

18. 139

19. 131

Explanation:

17. The question is asking for angle BEF. This angle is complementary to angle DEB, which means that when we add the two angles up, we get 90 degrees. Knowing this and knowing the value of angle DEB, we get 41 + BEF = 90. So we subtract 41 from both sides and we get BEF = 49.

18. The question is asking for angle CEB. We first get that CEF is 90 degrees because CED is a straight line, and DEF is 90 degrees, so CEF is also 90 degrees (90 + 90 = 180). CEB is just angle CEF and angle BEF added together and we have both. CEB = 90 + 49 = 139.

19. The question is asking for angle AEF. We first need to realize that angle AEC and DEB are equal. AEF is just equal to AEC + CEF, and now we have both. AEF = 41 + 90 = 131.