Question

The measure of angle of quardirateral (x-20) (x+20) (2x+5) (2x-5)​

Answer 1

${ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}$

• Measure of all angles of quadrilateral = (x - 20), (x+20), (2x+5) and (2x-5)

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• What are the angles of quadrilateral?

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

We know,

Sum of all angles of quadrilateral = 360

Given that,

Measure of all angles of quadrilateral = (x - 20), (x+20), (2x+5) and (2x-5)

According to the question :-

⟶ (x - 20) + (x+20) + (2x+5)+ (2x-5) = 360°

⟶ x + x + 2x + 2x + 20 - 20 + 5 - 5 = 360°

⟶ 6x = 360°

⟶ x = 60°

Now, find the measure of all angles of

quadrilateral

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1st angle = (x -20) = 60 - 20 = 40°

2nd angle = (x + 20) = 60 + 20 = 80°

3rd angle = (2x + 5) = 60 × 2 + 5 = 125°

4th angle = (2x - 5) = 60 × 2 - 5 = 115°

Hence,

measure of all angles of quadrilateral are

40°, 80° , 125°, 115°

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Verification :-

Given that,

Sum of all angles of quadrilateral = 360°

⟶ 40° + 80° + 125° + 115° = 360°

⟶ 360° = 360°

LHS = RHS

Hence, verified.