# Calculate the radian measures of the angles of a parallelogram if the angles adjacent to one side

July 31, 2021 | education

| **Calculate the radian measures of the angles of a parallelogram if the angles adjacent to one side of it are proportional to the numbers 2 and 5.**

We use the property of the sum of the angles of the AVSD parallelogram:

<A + <B = 180 = pi (in radian measure). (one)

We write down the ratio of the angles according to the condition of the problem: A / <B <= 2/5, or 5 * <A = 2 * <B, we express one angle through the other, we get:

<A = (2/5) * (<B) = 0.4 * (<B). Substituting this ratio into equation (1), we get:

0.4 * (<B) + (<B) = pi; 1.4 * (<B) = pi; (<B) = pi / 1.4 = 5 pi / 7;

<A = pi – 5 pi / 7 = 2 pi / 7.

Let’s check: A / <B <= 2/5; (2 pi / 7): (5 pi / 7) = 2/5.

Answer: <A = 2 pi / 7; <B = 5 pi / 7.

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