If m BCD = 21° and mEF = 33°, determine MABD using the appropriate theorems and postulates.

m(ar ABD) = 54°

Solution:

The image of the question is attached below.

Given data:

m∠BCD = 21° and m(ar EF) = 33°

By central angle theorem,

The measure of a central angle is equal to the measure of the intercepted arc.

m (ar EF) = m∠ECF

m∠EFC = 33°

By vertical angle theorem,

If two lines are intersecting, then vertically opposite angles are equal.

⇒ m∠ACB = m∠ECF

⇒ m∠ACB = 33°

m∠ACD = m∠ACB + m∠BCD

              = 33° + 21°

m∠ACD = 54°

By central angle theorem,

m(ar ABD) = m∠ACD

m(ar ABD) = 54°

because they could drop even lower..