In a convex quadrilateral ABCD, AB = BC, AD = CD, angle B = 97 degrees. Angle D = 111 degrees Find angle A.
| August 18, 2021 | education
Let’s draw a diagonal AC, which will divide the quadrilateral into two isosceles triangles ADC and ABC with the base AC.
Let’s define the angles at the base of the triangle ABC.
Angle BAC = BCA = (180 – ABC) / 2 = (180 – 97) / 2 = 83/2 = 41.5.
Determine the angles at the base of the triangle ADC.
Angle DАС = DСА = (180 – АDC) / 2 = (180 – 111) / 2 = 69/2 = 34.5.
Determine the value of the angle BAD.
Angle BAD = BAC + DAC = 41.5 + 34.5 = 76.
Answer: Angle A is 76.
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