The diagonal divides the corner of the rectangle in a ratio of 1: 8. Find the degree measure of the acute

The diagonal divides the corner of the rectangle in a ratio of 1: 8. Find the degree measure of the acute angle that forms when the diagonals of the rectangles intersect.

Let us denote by the variable n the number of degrees to which the smaller angle obtained by dividing the right angle by the diagonal is equal.

Then we can express the degree value of the larger angle as 8n.

Let’s write down the equation and calculate what the greater angle is equal to:

n + 8n = 90;

9n = 90;

n = 10;

90 – 10 = 80.

Let’s calculate what the acute angle will be equal to, which is obtained when the diagonals intersect, if we know that it is included in a triangle, where there are two angles of 80 ° each:

180 – 80 – 80 = 20.

Answer: The angle is 20 °.