The sides AB, BC, CD and AD of the quadrilateral ABCD contract the arcs of the circumscribed circle
| September 6, 2021 | education
The sides AB, BC, CD and AD of the quadrilateral ABCD contract the arcs of the circumscribed circle, the degree values of which are 93 °, 51 °, 114 °, 102 °, respectively. Find the corner B of this quadrilateral.
Construct the diagonal BD of the quadrilateral ABCD.
The inscribed angle ABD rests on the arc AD, the degree measure of which is 102 degrees, then the angle ABD is equal to half of the arc AD on which it rests.
Angle ABD = 102/2 = 51.
The inscribed angle ACD rests on the arc CD, the degree measure of which is 114 degrees, then the angle ACD is equal to half of the arc AC on which it rests.
Angle ACD = 114/2 = 57.
Then the angle ABC = ABD + ACD = 51 + 54 = 105.
Answer: Angle B of the quadrilateral ABCD is 105.
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