Given m∠DOE = 72° and m∠EOG = 84° in ⊙O. EF is a diameter. Find the following. (Give measures in degrees.) (a ) mDF (b) m∠F (c) m∠DGE (d) m∠EHG

Question

Consider the following figure.

Given m∠DOE = 72° and m∠EOG = 84° in ⊙O. EF is a diameter

Find the following. (Give measures in degrees.)

(a ) mDF

  

(b) m∠F

 

(c) m∠DGE

 

(d) m∠EHG

Answer 1

(a ) mDF = 180° - 72° = 108°;

(b) m∠F =72°/2 = 36°;

(c) m∠DGE = 72°/2 = 36°;

(d) m∠EHG = (84° + 108°)/2 = 96°.