The diagonal AC of the parallelogram ABCD forms with its sides angles of 25 ° and 30 °. Find a larger parallelogram angle

By the parallelogram property, ∠A = ∠C = 25 ° + 30 ° = 55 ° and ∠B = ∠D.
Find the angles B and D.
The sides AD and BC are parallel (by definition of a parallelogram). If we consider AC as secant to these parallel lines, then it becomes obvious that ∠DAC = ∠BCA = 30 ° (because they are lying crosswise).
Consider the triangle ABC.
By the theorem on the sum of the angles of a triangle, we can write: 180 ° = ∠CAB + ∠B + ∠BCA
180 ° = 25 ° + ∠B + 30 °
∠B = 125 ° = ∠D
125> 55, therefore the angles B and D are larger.
Answer: a larger angle is 125 °