Question

Quadrilateral ABCD is inscribed in a circle. m A is 64°, m B is (6x + 4)°, and m C is (9x - 1)°. What is m D?

Answer 1

Answer: Choice D) 98 degrees

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Explanation:

The quadrilateral is inscribed in the circle which means every corner point (A,B,C,D) is on the circle. No part of the quadrilateral is outside the circle. 

One property of inscribed quadrilaterals is that the opposite angles add to 180 degrees. So,
A+C = 180
B+D = 180

We know that
A = 64
B = 6x+4
C = 9x-1

Let's use angles A and C to find x
A+C = 180
64+9x-1= 180
9x+63 = 180
9x+63-63 = 180-63
9x = 117
9x/9 = 117/9
x = 13

Which helps us find angle B
B = 6x+4
B = 6*13+4
B = 78+4
B = 82 degrees

Then we can finally find angle D
B+D = 180
82+D = 180
82+D-82 = 180-82
D = 98 degrees