Question

A circle is shown. Points A, B, C, and D are on the circle. Lines connect 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 = °

Answer 1

angle b = 110

angle d = 70

Explanation:

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Answer 2

• ∠B = 110°
• ∠D = 70°

Explanation:

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

∠B +∠D = 180°

(3x -4)° +(2x -6°) = 180° . . . . substitute given expressions

5x = 190 . . . . . . . . . . . . . . . . divide by °, add 10

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

Then the angle measures are ...

∠B = (3·38 -4)° = 110°

∠D = (2·38 -6)° = 70°