Question

Measures of opposite angles of parallelogram are (4x-4)degree and (3x+6)degree. Find the measure of each angle.

Answer 1

Answer:

The angles are :-

∠P = 36°,∠Q = 144°, ∠R = 36° and ∠S = 144°

★ Solution:

Let the four angles of a Parallelogram be ∠P, ∠Q, ∠R, and ∠S and let the given opposite side be ∠P and ∠R

We know that,

Opposite angles of a Parallelogram are equal.

According the question,

⟹ 4x - 4 = 3x + 6

⟹ 4x - 3x = 6 + 4

⟹ x = 10

The value of x is 10

So,

• ( 4x - 4 )

= ( 4 × 10 - 4 )

= 40 - 4

= 36°

∴ ∠P = ∠R = 36° .........( opposite angles )

Let The other angle be x,

= x + 36° = 180°

= x = 180 - 36

= x = 144°

∴ ∠Q = ∠S = 144° .........( opposite angles )

★ Now, Verification

∠P + ∠Q + ∠R + ∠S = 360°

⟹ 36° + 144° + 36° + 144° = 360°

⟹ 180 + 180 = 360

⟹ 360 = 360

L.H.S = R.H.S

Hence, Proved.

★ Key Concepts

• A quadrilateral in which both pairs of opposite sides are parallel is called parallelogram.

• The properties of parallelogram are:-

1. Opposite angles are parallel.
2. Opposite angles are equal.
3. Opposite sides are equal.
4. Adjacent angles are supplementary.
5. The diagonals bisect each other.

Answer 2

Answer:

Angle A is 36°

Angle B is 144°

Angle C is 36°

Angle D is 144°

Step-by-step explanation:

$\Large{\underline{\rm{Given:}}}$

• Measures of opposite angles are (4x - 4)° and (3x + 6)°

$\Large{\underline{\rm{To\:Find:}}}$

• Measure of each angle in the parallelogram

$\Large{\underline{\rm{Solution:}}}$

➙ Here it is given that the opposite angles of a parallelogram are (4x - 4)° and (3x + 6)°.

➙ But we know that in a parallelogram, opposite angles are equal.

➙ Hence,

    4x - 4 = 3x + 6

    4x - 3x = 6 + 4

    x = 10

➙ Hence the value of x is 10.

➙ Now consider the angles of the parallelogram as A, B, C, D

➙ By given

    Angle A = 4x - 4

➙ Substitute the value of x,

    Angle A = 4 × 10 - 4 = 36°

➙ Hence Angle A is 36°

➙ Also by given,

    Angle C = 3x + 6

    Angle C = 3 × 10 + 6 = 36°

➙ Therefore Angle C is 36°

➙ Now we know that in a parallelogram, adjacent angles are supplementary.

➙ Hence,

    Angle A + Angle B = 180

    Angle B = 180 - 36

    Angle B = 144°

➙ Hence Angle B is 144°

➙ Now we know that Angle D is opposite to Angle B.

➙ Hence,

   Angle D = Angle B

   Angle D = 144°

➙ Therefore Angle D is 144°

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