MATH SOLVE

2 months ago

Q:
# 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?A. 64°B. 82°C. 90°D. 98°E. 116°

Accepted Solution

A:

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

============================================================

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