m(ar ABD) = 57°
Solution:
The given question have mistake. The correct question is wiiten below.
If angle BCD = 23° and arc EF = 34°, determine arc abd using the appropriate theorems and postulates.
Given data:
m∠BCD = 23° and m(ar EF) = 34°
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∠ECF = 34°
By vertical angle theorem,
If two lines are intersecting, then vertically opposite angles are equal.
⇒ m∠ACB = m∠ECF
⇒ m∠ACB = 34°
m∠ACD = m∠ACB + m∠BCD
= 34° + 23°
m∠ACD = 57°
By central angle theorem,
m(ar ABD) = m∠ACD
m(ar ABD) = 57°
