Question

PINK is a rhombus with angle IPk = 64 degree. find angle IKN​

Answer 1

Question :-

PINK is a rhombus with ∠ IPK = 64° . find ∠ IKN .

Solution :-

∵ all sides of rhombus are equal to each other

∴ P K = I K

and so,

∠ PKI = ∠ PIK  ( angles opp. to equal sides )

Now,

By angle sum property of triangle

In Δ PIK

→  ∠ PIK + ∠ PKI + ∠ KPI = 180°

→  2 ∠ PIK + 64° = 180°

→  2 ∠ PIK = 180° - 64°

→    ∠ PIK = 58°

Now,

∵ opposite sides of rhombus are parallel to each other

∴ PI ║ KN

so,

∠ PIK = ∠ IKN = 58°  (alternate interior angles)

Hence,

∠ IKN = 58° .

________________________

Definition of rhombus :-

Rhombus is a quadrilateral with all sides equal .

Properties of rhombus :-

• Rhombus have all sides equal .
• opposite angles of rhombus are equal.
• adjacent angles of rhombus are supplementary .
• A rhombus is a parallelogram whose diagonals bisect each other at right angle .

Important formula related to rhombus :-

• perimeter of rhombus

perimeter of rhombus = 4 × ( side )  units

• area of rhombus

ar (rhombus) = 1/2 × d₁ × d₂

( where d₁ and d₂ are diagonals of rhombus ).

Answer 2

Answer:

58 is the right answer buddy