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lbvjy [14]
2 years ago
6

Help help help please I beg you it’s a circle geometry wuestion

Mathematics
1 answer:
WITCHER [35]2 years ago
4 0

Answers:

  • a = 64
  • b = 112
  • c = 78
  • d = 88

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

Explanation:

The 102 inscribed angle cuts off the arc that's composed of the 140 and 'a'.

Due to the inscribed angle theorem, we know that a+140 is exactly equal to twice that of 102.

This means,

a+140 = 2*102

a+140 = 204

a = 204-140

a = 64

-----------------

The angles 102 and c are inscribed angles opposite one another. They add to 180. This is true for any inscribed quadrilateral.

c+102 = 180

c = 180-102

c = 78

-----------------

Another useful rule is that the four angles of any quadrilateral always add to 360.

102+92+c+d = 360

102+92+78+d = 360

272+d = 360

d = 360-272

d = 88

-----------------

The inscribed angle d cuts off the arc a+b

This means 2d is the measure of a+b because of the inscribed angle theorem.

a+b = 2d

64+b = 2*88

64+b = 176

b = 176-64

b = 112

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