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

Question

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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] · Answer 1 · 2021-12-17T15:16:11+03:00

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.