# In the trapezoid ABCD AB = CD, AC = AD and ∠ABC = 95 °. Find the CAD angle. Since AB = CD, then the trapezoid ABCD is isosceles.
Then, by the property of an isosceles trapezoid, ∠ABC = ∠BCD = 95 ° and ∠CDA = ∠DAB.
Recalling that the sum of the angles of a convex n-gon is calculated by the formula (n-2) 180 °, we find that the sum of the angles of the trapezoid is (4-2) 180 ° = 360 °.
Then ∠ABC + ∠BCD + ∠CDA + ∠DAB = 360 °
95 ° + 95 ° + ∠CDA + ∠DAB = 360 °
∠CDA + ∠DAB = 170 °
∠CDA = ∠DAB = 170 ° / 2 = 85 °
Consider the triangle ACD.
Since AC = AD, this triangle is isosceles.
Therefore, by the property of an isosceles triangle, ∠CDA = ∠DCA = 85 °
∠BCA = ∠BCD-∠DCA = 95 ° -85 ° = 10 °
∠CAD = ∠DCA = 10 ° (because they are cross-lying for parallel lines AD and BC). 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.