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motikmotik
3 years ago
6

Applying the Third Corollary to the Inscribed Angles Theorem A circle is shown. Points A, B, C, and D are on the circle. Lines c

onnect each point to form a quadrilateral. Angle B is (3 x minus 4) degrees and angle D is (2 x minus 6) degrees. The measure of ∠B is (3x – 4 )° and the measure of ∠D is (2x – 6)°. What are the measures of angles B and D? m∠B = ° m∠D = °
Mathematics
1 answer:
Marat540 [252]3 years ago
8 0

Answer:

  • ∠B = 110°
  • ∠D = 70°

Step-by-step explanation:

Opposite angles in an inscribed quadrilateral are supplementary, so ...

  ∠B +∠D = 180°

  (3x -4) +(2x -6) = 180

  5x = 190 . . . . . . . . . . . add 10, collect terms

  x = 38 . . . . . . . . . . . . . divide by 5

  ∠D = 2(38) -6 = 70

  ∠B = 180 -70 = 110

The measures of angles B and D are 110° and 70°, respectively.

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