# HELP MATH EXAM TMR? Relevance
• 19.

20.

21.

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• Opposite angles of a cyclic quadrilateral are supplementary. That should get you through all of those questions, but I do still have one concern.

Those given angle measures appear to be in degrees, but no units are given. Normally that is done only for radian measure. The copyright date looks like 1990. Is that how Addison-Wesley still does things? As we say here, that is wrong, with a capital R.

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• 19.

The sum of two opposite angles of concyclic quadrilateral is 180°.

m∠B + m∠D = 180

m∠B + 80 = 180

m∠B = 100

m∠C + m∠A = 180

m∠C + 110 = 180

m∠C = 70

====

20.

m∠A + m∠C = 180

m∠A + 75 = 180

m∠A = 105

m∠D + m∠B = 180

m∠D + 90 = 180

m∠D = 90

====

21.

m∠B + m∠D = 180

m∠B + (2/3)m∠B = 180

(5/3)m∠B = 180

m∠B = 108

m∠D = (2/3)m∠B

m∠D = (2/3) * 108

m∠D = 72

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• since angle A and angle C have the same end points (B and D) and those end points are also on the circle, this means A and C are equal.  Same for D and B.

Can you figure it out from there?

• Justin asks too many question each day

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