# In a convex quadrilateral ABCD AB = BC, AD = CD, ∠B = 100 °, ∠D = 104 °. Find the angle A

May 31, 2020 | Education

| Draw the diagonal AC.

Consider the triangle ABC.

Since AB = BC, it means that the triangle ABC is isosceles.

By the theorem on the sum of the angles of a triangle:

180 ° = ∠B + ∠BAC + ∠BCA.

180 ° = 100 ° + ∠BAC + ∠BCA.

80 ° = ∠BAC + ∠BCA.

By the property of an isosceles triangle, ∠BAC = ∠BCA, then

∠BAC = ∠BCA = 80 ° / 2 = 40 °.

The ACD triangle is also isosceles.

By similar calculations we get: 180 ° = 104 ° + ∠DAC + ∠DCA.

∠DAC + ∠DCA = 76 ° / 2 = 38 °

∠A = ∠BAC + ∠CAD = 40 ° + 38 ° = 78 °

Answer: 78

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.