Question

Please answer this Fill in the Blanks Correctly

Answer 1

1. Bisect

2. 130 Degrees

According to the given details

Three angles of a quadrilateral are 75°, 90° and 65°

Let us assume the fourth angle to be x.

We know that according to the quadrilateral angle sum property, the sum of all the four interior angles is 360 degrees.

Sum of all angles of a quadrilateral = 360°

⇒ 75° + 90° + 65° + x = 360°

⇒ 230° + x = 360°

⇒ x = 360° – 230°

⇒ x = 130°

Hence, the fourth angle is 130°.

3. Supplementary angles to each other (that means they add up to 180 degrees)

4. Rectangle

5. Square

6. 50 Degrees

ABCD is a rhombus. We know that diagonals of rhombus bisect each other perpendicularly.

Hence, ∠BOC= 90∘

 ∠OCB = 40∘

  (Given)

AD∥BC and BD is the transversal   --- (Opposite sides of rhombus are parallel to each other)

∴ ∠ADB = ∠DBC   ---- (Alternate angles)

In △OBC,

∠BOC + ∠OCB + ∠OBC = 180∘

 ⇒  90∘  + 40    + ∠OBC = 180∘

⇒  ∠OBC =180∘  - 130∘

 ∴  ∠OBC = 50∘

But ∠OBC =∠DBC

∴  ∠ADB = 50  ∘ ---( Alternate angle)

7. 50 Degrees

In △BOC,  

∠OBC=∠OCB  ----- (Opposite angle of isosceles triangle)

∠OBC+∠OCB+∠BOC=180∘

 25∘ +25∘  +∠BOC=180∘

 Therefore, ∠BOC=130∘

So, ∠AOB+∠BOC=180∘  --------(Linear pair)

∠AOB=180∘  − 130∘

 ∠AOB=50∘

 So, the acute angle between the diagonal is 50∘

8. Rectangle

9. Square

10. Isosceles Triangle

Answer 2

1-8 are correct in above answer

but

9. rectangle

10. equilateral triangle