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atroni [7]
3 years ago
9

Quadrilateral ABCD ​ is inscribed in this circle.

Mathematics
2 answers:
Fofino [41]3 years ago
7 0
By the Inscribed Quadrilateral Theorem, a quadrilateral can only be inscribed if and only if opposite angles are supplementary.  This means that \angle D \text{ and } \angle B are supplementary, or add up to 180°.  This gives us the equation
(3<em>x</em> + 9)° + (2<em>x</em> - 4)° = 180°
Combine like terms:
5<em>x</em> + 5 = 180
Subtract 5 from each side:
5<em>x</em> + 5 - 5 = 180 - 5
5<em>x</em> = 175
Divide both sides by 5:
5<em>x</em>/5 = 175/5
<em>x</em> = 35
This means that m \angle D=3(35)+9=114&#10;\\m \angle B=2(35)-4 = 66&#10;\\m \angle A=2(35) + 3=73
We take these 3 angles away from 360 and we will have the measure of angle C:
360 - 114 - 66 - 73 = 107°<em />
enot [183]3 years ago
6 0

Answer:

62 is the answer for my k12 freinds

Step-by-step explanation:

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