Question

a diagonal of rectangle is inclined to one side of the rectangle at 20° find the acute angle between the diagonals

Answer 1

Draw the rectangle (let's call it ABCD), and its two diagonals (the intersection being E) such that angle CDE is 20 degrees.

Let's focus on the triangle CDE.

Angle CDE is 20 degrees, and the angle DCE is also 20 degrees because all rectangles are, by definition, symmetric.

The angles of a triangle add up to 180 degrees, so the angle DEC would be 180 - (20 + 20) = 140.

Angle DEC is the obtuse angle between the diagonals. The acute angle and the obtuse angle between the diagonals are supplementary, so they must add up to 180 degrees.

So, the acute angle between the diagonals is 180 - 140 = 40 degrees.

Answer 2

.

As ABCD is a rectangle and each angle of a rectangle is 90°,

∴∠ ADC = 90°

⇒∠ ADB + ∠ BDC = 90°

⇒∠ ADB + 25°   = 90°

∴∠ ADB = 90° - 25°

=  65°