Question

The measure of two adjacent angle of a parallelogram are in the ratio 4:5. the angle are​



solve fast plsss​

Answer 1

Let ∠A and ∠B are two adjacent angles.

But we know that the sum of adjacent angles of a parallelogram is 180⁰.

⠀⠀⠀⠀⠀⠀⠀∠A + ∠B = 180⁰

Given that adjacent angles of a parallelogram are in the ratio 4 : 5 and let the ratio be multiple of x .

⠀⠀⠀⠀⠀⠀⠀∠A + ∠B = 180⁰

⇒ 4x + 5x = 180⁰

⇒ 9x = 180⁰

⇒ $\frac{180}{9}$

⇒ x = 20⁰

⠀⠀⠀⠀⠀⠀⠀∠A = 4x = 4 × 20 = 80⁰

⠀⠀⠀⠀⠀⠀⠀∠B = 5x = 5 × 20 = 100⁰

Also ∠B + ∠C = 180⁰ [Since ∠B and ∠C are adjacent angles]

⇒ 100⁰ + ∠C = 180⁰

⇒ ∠C = 180⁰ - 100⁰ = 80⁰

Now, ∠C + ∠D = 180⁰ [Since ∠C and ∠D are adjacent angles]

⇒ 80⁰ + ∠D = 180⁰

⇒ ∠D = 180⁰ - 80⁰ = 100⁰

Answer 2

Answer:

Let ∠A and ∠B are two adjacent angles.

But we know that the sum of adjacent angles of a parallelogram is 180⁰.

⠀⠀⠀⠀⠀⠀⠀∠A + ∠B = 180⁰

Given that adjacent angles of a parallelogram are in the ratio 4 : 5 and let the ratio be multiple of x .

⠀⠀⠀⠀⠀⠀⠀∠A + ∠B = 180⁰

⇒ 4x + 5x = 180⁰

⇒ 9x = 180⁰

⇒ 180/9

⇒ x = 20⁰

⠀⠀⠀⠀⠀⠀⠀∠A = 4x = 4 × 20 = 80⁰

⠀⠀⠀⠀⠀⠀⠀∠B = 5x = 5 × 20 = 100⁰

Also ∠B + ∠C = 180⁰ (Since ∠B and ∠C are adjacent angles)

⇒ 100⁰ + ∠C = 180⁰

⇒ ∠C = 180⁰ - 100⁰ = 80⁰

Now, ∠C + ∠D = 180⁰ [Since ∠C and ∠D are adjacent angles]

⇒ 80⁰ + ∠D = 180⁰

⇒ ∠D = 180⁰ - 80⁰ = 100⁰

$\huge \underline \mathtt \colorbox{cyan}{A, D 100°}$

$\huge \underline \mathtt \colorbox{cyan}{B, C 80°}$

$\bold{\huge{\fbox{\color{Maroon}{Hope it helps you}}}}$

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