PLEASE HURRY Quadilateral abcd is inscribed in circle z such that AB is parallel to DC and m

Mathematics

1 answer:

frozen [14]3 years ago

4 0

Answer:

41°

Step-by-step explanation:

Looking at the attached diagram

A central angle of a circle is always congruent to its intercepted arc.

Therefore, m arc BC = m∠BZC

Again, m∠BAC is one-half m arc BC, as the measure of an inscribed angle is half the measure of its intercepted arc.

This gives us the following results:

= m∠BZC = 82°

= m arc BC = m∠BZC

= m arc BC = 82°

= m∠BAC = 1/2 × 82°

= m∠BAC = 41°

Note that:

∠DCA ≅ ∠BAC because alternate interior angles are congruent.

So m∠DCA = m∠BAC.

Hence, m∠DCA = 41°.

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