Answer:
41°
Step-by-step explanation:
First note that m arc BC = m∠BZC
The reason is because a central angle of a circle is always congruent to its
intercepted arc.
Also m∠BAC is one-half m arc BC, as the measure of an inscribed angle is half the measure of its intercepted arc.
Hence, the calculation is given below:
m∠BZC = 82°
m arc BC = m∠BZC
m arc BC = 82°
m∠BAC = 1/2 × 82°
m∠BAC = 41°
It is important to note that
∠DCA ≅ ∠BAC because alternate interior angles are congruent.
So m∠DCA = m∠BAC.
Therefore, m∠DCA = 41°.
