Question

The opposite angles of a parallelogram are (2x – 3)° and (45 – x)° , then find the value of

‘x’ .Also find all the angles of parallelogram ​

Answer 1

GivEn:

• Adjacent angles = (2x – 3)° and (45 – x)°.

To find:

• The value of x.

Solution:

• Let the four angles of parallelogram be ∠A, ∠B, ∠C and ∠D.

Here, Opposite angles are,

• (2x – 3)°(∠A)
• (45 – x)°(∠C)

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« Now, Finding the value of x,

As we know that,

• Opposite angles of //gm are equal.

∴ 2x – 3 = 45 – x

→ 2x + x = 45 + 3

→ 3x = 48

→ x = 48/3

→ x = 16

Therefore,

• (2x – 3) = 2(16) - 3 = 29°
• 45 – x = 45 – 16 = 29°

∴ Hence, ∠C = ∠A

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« Now, Finding angles of the //gm,

As we know that,

• Sum of two adjacent angles of a parallelogram is 180°.

∴ ∠A + ∠B = 180°

→ 29° + ∠B = 180°

→ ∠B = 180° - 29°

→ ∠B = 151°

∠B = ∠D = 151° (Opposite angles are equal)

∴ Hence, All angles of the parallelogram are 29°, 151°, 29° & 151°.

Answer 2

Answer:

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