The diagonal BD of the parallelogram ABCD forms angles of 25 ° and 110 ° with its sides. Find a smaller parallelogram angle

By the parallelogram property, ∠B = ∠D = 25 ° + 110 ° = 135 ° and ∠A = ∠C.
Find the angles A and C.
The sides AD and BC are parallel (by definition of a parallelogram). If we consider BD as secant to these parallel lines, it becomes obvious that ,CBD = ∠ADB = 110 ° (since they are lying crosswise).
Consider the triangle ABD.
By the theorem on the sum of the angles of a triangle, we can write: 180 ° = ∠ABD + ∠BDA + ∠A
180 ° = 25 ° + 110 ° + ∠A
∠A = 45 ° = ∠C
135> 45, therefore the angles A and C are smaller.
Answer: a smaller angle is 45 °.