# A circle is described around the trapezoid, one of whose angles is 49 °. Find the rest of the trapezoid angles

May 31, 2020 | Education

| The circle can be described only near an isosceles trapezoid (by the trapezoid property).

It turns out that our trapezoid is isosceles (or isosceles).

Let 49 ° be the angle BAD.

∠BAD = ∠ADC = 49 ° (by the property of an isosceles trapezoid).

The sum of the angles of a convex n-gon is calculated by the formula (n-2) 180 °, then the sum of the angles of the trapezoid is (4-2) 180 ° = 360 °.

360 ° = ∠BAD + ∠ADC + ∠DCB + ∠CBA

360 ° = 49 ° + 49 ° + ∠DCB + ∠CBA

∠DCB + ∠CBA = 262 °

∠DCB = ∠CBA (by the property of an isosceles trapezoid).

Then ∠DCB = ∠CBA = 262 ° / 2 = 131 °

Answer: ∠DCB = ∠CBA = 131 °, ∠BAD = ∠ADC = 49

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