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

May 31, 2020 | Education

| 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 °

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.