Question

PLEASE HURRY
Quadrilateral ABCD is inscribed in OZ such that AB | DC and Find m

Answer 1

41°

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°.