In a convex quadrilateral ABCD AB = BC, AD = CD, angle B = 69 degrees, angle D = 135 degrees! Find angle A.

Consider a quadrilateral ABCD:

angle B = 69 °, angle D = 135 °;

Let’s draw a diagonal AC.

We have 2 triangles: ABC and ADC.

Consider a triangle ABC:

angle B = 69 °, AB = BC, therefore, angle BAC = angle BCA = (180 ° – 69 °): 2 = 55.5 °.

Consider triangle ADC:

angle D = 135 °, CD = AD, therefore angle DAC = angle ACD = (180 ° – 135 °): 2 = 22.5 °.

Angle A = angle BAC + angle CAD = 55.5 ° + 22.5 ° = 78 °.

Answer: angle A = 78 °.