Question

Angles of quadrilateral are /_ A = ( 3x - 5)° , /_ B= ( 8x - 15) ° , /_ C= ( 2x + 4) ° and /_ D= 90° , find the value of x.​

Answer 1

Given

Angles of quadrilateral are

• ∠A = (3x - 5)°

• ∠B = (8x - 15)°

• ∠C = ( 2x + 4 )°

• ∠D = 90°

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To Find

We have to find the value of x.

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Concept Using

The Sum of interior angles of quadrilaterals is 360°.

• ∠A + ∠B + ∠C + ∠D = 360°

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Solution

(3x - 5)° + (8x - 15)° + ( 2x + 4 )° + 90° = 360°

Now , Opening brackets and simplifying

⇛3x - 5° + 8x - 15° + 2x + 4° + 90° = 360°

⇛13x + 74° = 360°

⇛13x = 360° - 74°

⇛13x = 286°

⇛x = 286° ÷ 13

⇛x = 22

☛ Putting the values

⇥∠A = (3x - 5)°

⇥ (3 × 22 - 5)°

⇥(66 - 5)°

⇥∠A = 61°

⇥∠B = (8x - 15)°

⇥(8 × 22 - 15)°

⇥(176 - 15)°

⇥∠B = 161°

⇥∠C = ( 2x + 4 )°

⇥(22 × 2 + 4)°

⇥(44 + 4)°

⇥∠C = 48°

⇥∠D = 90°

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Verification

The Sum of interior angles of quadrilaterals is 360°.

• ∠A + ∠B + ∠C + ∠D = 360°

⇨61° + 161° + 48° + 90° = 360

⇨222° + 138° = 360°

⇨360° = 360°

LHS = RHS