Quadrilateral ABCD is inscribed in this circle.
2 answers:
By the Inscribed Quadrilateral Theorem, a quadrilateral can only be inscribed if and only if opposite angles are supplementary. This means that 
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
We take these 3 angles away from 360 and we will have the measure of angle C:
360 - 114 - 66 - 73 = 107°<em />
(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
We take these 3 angles away from 360 and we will have the measure of angle C:
360 - 114 - 66 - 73 = 107°<em />
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