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

May 31, 2020 | Education

| 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 °.

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