SOLUTION: Assume quadrilateral ABCD is inscribed in a circle. If {{{m<A = x^2}}}, {{{m<B = 9x - 2}}}, and {{{m<C = 11x}}}, find x and the measure of angle D.

Question 1029748: Assume quadrilateral ABCD is inscribed in a circle. If , , and , find x and the measure of angle D.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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Assume quadrilateral ABCD is inscribed in a circle. If , , and , find x and the measure of angle D.
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If a quadrilateral is inscribed in a circle, then its opposite angles sum up to 180�.

In other words, If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

I think if the teacher gave you this problem, you should be familiar with this fact. 
If not, you can read about it in the lesson A property of the angles of a quadrilateral inscribed in a circle in this site.

OK. Based on this fact, you can write an equation for the opposite angles A and C

 = ,   or

 = .

Factor left side:

(x-9)*(x+20) = 0.

The only positive root is x = 9.

Hence, angle A is 81� and angle C is 11*9� = 99�. (which is not so important for us now).

What is really important, it is the fact that angle B is 9*9�-2� = 79�.

Then the opposite to B angle D = 180� - 79� = 101�.

Answer. Angle D has the measure of 101�.

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