Question

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Q1. If one side of a parallelogram is 36 less than twice adjacent sides. Then find the angle​

Answer 1

Answer :

›»› The angles of a parallelogram is 72°, 108°, 72°, and 108° respectively.

Given :

• One side of a parallelogram is 36 less than twice adjacent sides.

To Find :

• The angles of a parallelogram.

Solution :

Let us assume that, the adjacent angle is "x".

As it is given that, one side of a parallelogram is 36 less than twice adjacent sides.

→ (2x - 36)°.

According to the given question,

As we know that

The sum of all adjacent sides of a parallelogram is 180°.

→ x + (2x - 36) = 180

→ x + 2x - 36 = 180

→ 3x - 36 = 180

→ 3x = 180 + 36

→ 3x = 216

→ x = 216/3

→ x = 72

Therefore,

The angles of a parallelogram will be,

• x = 72°.
• (2x - 36) = (2 * 72 - 36) = 144 - 36 = 108°.

Now, we know that, opposite angles of a parallelogram are equal. So,

• 72° = 72°.
• 108° = 108°.

Hence, the angles of a parallelogram is 72°, 108°, 72°, and 108° respectively.

Verification :

The sum of all four angles of a parallelogram is 360°.

→ 72 + 108 + 72 + 108 = 360

→ 180 + 72 + 108 = 360

→ 180 + 180 = 360

→ 369 = 360

Clearly, LHS = RHS.

Here both the conditions satisfy, so our answer is correct.

Hence Verified !

Answer 2

Answer:

Given :-

• One side of a parallelogram is 36 less than twice adjacent sides .

To Find :-

• What is the angles .

Solution :-

» Let, one of the angle be x

» And, the other angle be 2x - 36

We know that,

★ The sum of adjacent sides = 180° ★

➣ According to the question,

⇒ x + 2x - 36° = 180°

⇒ 3x = 180° + 36°

⇒ 3x = 216°

⇒ x = $\sf\dfrac{\cancel{216°}}{\cancel{3}}$

➠ x = 72°

Hence, the other angles required :-

➟ One angles is 72°

➟ Other angle will be 2x - 36 = 2(72) - 36 = 108°

$\therefore$ The angles of parallelogram are 108°, 72°, 108° and 72° .

Let's us verify the answer,

We know that,

✪ Sum of four parallelogram = 360° ✪

⇒ 108° + 72° + 108° + 72° = 360°

⇒ 180° + 180° = 360°

➠ 360° = 360°

Hence, Verified .