Question

The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle is 50º. The two adjacent angles of a 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∘