Question

the 2 acute angles of a parallelogram are 45°. find the 2 obtuse​

Answer 1

Answer:

obtuse angles are 180-45=135

Answer 2

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

∘

a