Question

what is the sum of each interior angle in a (Quadrilateral) whose measures are 96 degree,84 degree, 2x and x ?​

Answer 1

Given:-

• ∠A = 96°
• ∠B = 84°
• ∠C = 2x
• ∠D = x

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To Find:-

• The value of x.

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Solution:-

According to the question,

We know that,

• The sum of all interior angle in quadrilateral is 360°.

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→ ∠A + ∠B + ∠C + ∠D = 360°

→ 96° + 84° + 2x + x = 360°

→ 180° + 3x° = 360°

→ 3x = 360° - 180°

→ 3x = 180

→ x = 180/3

→ x = 60°

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Hence,

• ∠A = 96°
• ∠B = 84°
• ∠C = 2 × 60° = 120°
• ∠D = 60°

Answer 2

Given

• Angles of a quadrilateral :-
• ∠A = 96°
• ∠B = 84°
• ∠C = 2x°
• ∠D = x°

To find

• Sum of each interior angle in the quadrilateral.

Solution

• ∠A + ∠B + ∠C + ∠D = 360°

Since, the sum of all the interior angles in a quadrilateral is equal to 360°

• 96° + 84° + 2x° + x° = 360°
• 180° + 3x° = 360°
• 3x° = 360° - 180°
• 3x° = 180°
• x° = 180°/3
• x° = 60°

Therefore the angles of the quadrilateral are :-

• ∠A = 96°
• ∠B = 84°
• ∠C = 2x° = 2(60)° = 120°
• ∠D = x° = 60°

Verification

• ∠A + ∠B + ∠C + ∠D = 360°
• 96° + 84° + 120° + 60° = 360°
• 180° + 180° = 360°
• 360° = 360°
• L.H.S = R.H.S