Given: m∠DOC = 113°; m∠DOE = 8°
If ∠BOD and ∠DOE are complementary angles, then what is the measure of ∠BOC?
Complementary angles are two angles that add up to 90 degrees.
If ∠BOD and ∠DOE are complementary angles, then we have:
m∠BOD + m∠DOE = 90 degrees
m∠BOD + 8 = 90
m∠BOD = 90 - 8
m∠BOD = 82 degrees
Now, we know that m∠BOC + m∠BOD = 180 degrees (because they are adjacent angles on a straight line).
Substituting the known value of m∠BOD, we have:
m∠BOC + 82 = 180
m∠BOC = 180 - 82
m∠BOC = 98 degrees
Therefore, the measure of ∠BOC is 98 degrees.