In a convex quadrilateral ABCD, the angle B = 21 degrees, the angle D is 125 degrees, AB = BC AD = CD.

In a convex quadrilateral ABCD, the angle B = 21 degrees, the angle D is 125 degrees, AB = BC AD = CD. find corner A.

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 – 21) / 2 = 159/2 = 79.5.

Determine the angles at the base of the ADS triangle.

Angle DАС = DСА = (180 – АDC) / 2 = (180 – 125) / 2 = 55/2 = 27.5.

Determine the value of the angle BAD.

Angle BAD = BAC + DAC = 79.5 + 27.5 = 107.

Answer: Angle A is 107.