Find a larger angle of the isosceles trapezoid ABCD if the diagonal of the AC forms with the base AD and the side AB the angles of 25 ° and 40 °, respectively
By the property of an isosceles trapezoid, the angles at the base are equal. Then ∠CDA = ∠BAD = 40 ° + 25 ° = 65 °.
AD || BC (by the definition of a trapezoid), then side AB can be considered as secant to these parallel lines.
Therefore, ∠DAB + ∠ABC = 180 ° (because these angles are internal one-sided) => ∠ABC = 180 ° -∠DAB = 180 ° -65 ° = 115 °.
∠BCD = ∠DAB = 115 ° (by the property of an isosceles trapezoid).
Therefore, these are the larger angles of the trapezoid.
Answer: a larger trapezoid angle = 115 °
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