Question

two consecutive angles of a parallelogram are (x+50) and (2x+10) then the special name we can give to this parallelogram is


pls show step nd diagram

Answer 1

Question:-

The two consecutive angles of a parallelogram are (x+50) and (2x+10) then the special name we can give to this parallelogram is ___.

Answer:-

The name of this type of parallelogram is Rectangle.

Now, Let's prove that, given the type of parallelogram is Rectangle.

Step-by-step explanation:-

Given that, The two consecutive angles of a parallelogram are (x+50) and (2x+10)

We know that,

• The consecutive angles of a parallelogram is 180°

Let, ∠A and ∠B be ( x + 50 ) and ( 2x + 10 ) respectively.

∴ ( x + 50 ) + ( 2x + 10 ) = 180°

: ⟹ x + 2x = 180 - 50 - 10

: ⟹ 3x = 180 - 60

: ⟹ 3x = 120

: ⟹ x = 120/3

: ⟹ x = 40

Now, the value of ( x + 50 )°

⟹ ( 40 + 50 )°

⟹ 90°

The value of ( 2x + 10 )°

⟹ ( 2 × 40 + 10 )°

⟹ ( 80 + 10 )°

⟹ 90°

So, ∠A = ∠C and ∠B = ∠D .....( opposite angles )

∴ A parallelogram each whose angles measures 90° is called rectangle.

Hence, Proved.