keljason15
keljason15 keljason15
  • 17-03-2021
  • Mathematics
contestada

Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show
your work.

Quadrilateral ABCD is inscribed in a circle Find the measure of each of the angles of the quadrilateral Show your work class=

Respuesta :

mhanifa
mhanifa mhanifa
  • 17-03-2021

Answer:

  • A= 94°, B = 102°, C = 86°, D = 78°

Step-by-step explanation:

ABCD is a cyclic quadrilateral

It has the property that opposite angles are supplementary: A with C and B with D.

Solve following for x:

  • x + 6 + x - 2 = 180°
  • 2x + 4 = 180°
  • 2x = 176°
  • x = 88°

The angles are:

  • A = 88° + 6° = 94°
  • C = 180° - 94° = 86°
  • D = 88° - 10° = 78°
  • B = 180° - 78° = 102°

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