Question

If angle bdc=23 and arc ef=34, determine arc abd using the appropriate theorems and postulates.

Answer 1

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°