The angle B of the quadrilateral ABCD inscribed in the circle is 40 °. Find the angle D of this quadrilateral.
| June 16, 2021 | education
A convex quadrilateral can be inscribed in a circle only when the sum of its opposite angles is 180 degrees.
In a quadrilateral ABCD, angles B and D are opposite, then their sum is 180 degrees:
angle B + angle D = 180 degrees;
40 + angle D = 180;
angle D = 180 – 40;
angle D = 140 degrees.
Answer: angle D = 140 degrees.
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