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Answer 1

★Given:-

• In parallelogram ABCD, ∠A=3 times ∠B.
• AB=5x-7
• CD=3x+1

★To find:-

• All the angles of parallelogram.
• Length of CD.

★Solution:-

Let ∠B = x

Then, as it is given that ∠A is 3 times of  ∠B,

• ∠A = 3x.

We know,

✦Opposite sides of a parallelogram are equal.

Therefore,

∠A = ∠C = 3x

∠B = ∠D = x.

We also know,

✦Sum of the angles of a parallelogram is equal to 360°.

Therefore,

∠A + ∠B + ∠C + ∠D = 360°

We have,

• ∠A = 3x
• ∠B = x
• ∠C = 3x
• ∠D = x

Putting values,

➔3x + x + 3x + x = 360°

➔8x = 360°

➔x = 45°.

Now,

➔∠A = 3x

        = 3(45)

        = 135°

➔∠B = x

         = 45°

➔∠C = 3x

         = 135°

➔∠D = x

         = 45°

Hence,the angles are 135°,45°,135°,45°.

Given,

• AB = 5x - 7
• CD = 3x + 1

✦As the opposite sides of a parallelogram are equal,

➔AB = CD

➔5x - 7 = 3x + 1

➔2x = 8

➔x = 4.

Substituting values of x in CD,

➔3x + 1

➔3(4) + 1

➔13.

Therefore,

The length of CD is 13.

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Know more:-

Properties of parallelogram:

• Opposite sides are congruent
• Opposite angels are congruent
• Diagonals bisect each other.
• Consecutive angles are supplementary
• If one angle is right, then all angles are right.
• Each diagonal of a parallelogram separates it into two congruent triangles.

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Answer 2

Given :

In parallelogram ABCD, ∠A = 3 times ∠B.

AB = 5x - 7 and CD = 3x + 1

To find :

• All the angles of llgm ABCD
• Length of CD

Solution :

• Properties of parallelogram

(★) Opposite sides of a parallelogram are equal

(★) Opposite angles of a parallelogram are equal

(★) Diagonals of a parallelogram bisect each other.

Let's solve the question

• ∠A = 3 times ∠B.

Let ∠A be x and ∠B be 3x

According to properties of llgm

• ∠A = ∠C = x
• ∠B = ∠D = 3x

Focus Zone : Sum of angles of a quadrilateral is 360°

→ ∠A + ∠B + ∠C + ∠D = 360°

→ x + 3x + x + 3x = 360

→ 2x + 6x = 360

→ 8x = 360

→ x = 360/8

→ x = 45°

•°• ∠A = ∠C = x = 45°

•°• ∠B = ∠D = 3x = 45 × 3 = 135°

As we know that opposite side of llgm are equal

• AB = 5x - 7
• CD = 3x + 1

→ AB = CD

→ 5x - 7 = 3x + 1

→ 5x - 3x = 7 + 1

→ 2x = 8

→ x = 8/2

→ x = 4

•°• CD = (3x + 1) = 3 × 4 + 1 = 13 unit

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