Question

The angle
between the two altitudes of a
parallelogram through the vertex of an
Obtuse angle of the parallelogram is 45°
Find the angles
of the parallelogram.​

Answer 1

Step-by-step explanation:

Let ABCD be a parallelogram where BE and BF are the perpendiculars through the vertex B to the sides DC and AD respectively.

Let,

∠A=∠C=x

∠B=∠D=y

Now,

∠A+∠B=180

[Adjacent angles]

⇒x+∠ABF+∠FBE+∠EBC=180

⇒x+(90−x)+45+(90−x)=180

⇒x−x−x+90+90+45=180

⇒−x=180−225

⇒x=45

∴∠A=∠C=45

∠B=(90−45)+45+(90−45)

=45+45+45

=135=∠D

Hence, the angles of the parallelogram are 45, 135, 45 and 135∘.