Question

The angles of a quadrilateral are 5x°,(3x+10)°,(6x-20°) and (x+25)°.find the value of x and measure of each angle of the quadrilateral *
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Answer 1

Answer:

The sum of all the angles of a quadrilateral is 360°.

5x + 3x + 10 + 6x - 20 + x + 25 = 360°

or, 15x + 15 = 360°

or, 15x = 360 - 15

or, x = 345/15

or, x = 23

5x = 5(23) = 115°

3x + 10 = 3(23) + 10 = 79°

6x - 20 = 6(23) - 20 = 108°

x + 25 = 23 + 25 = 48°

Answer 2

$\huge\mathfrak\blue{Answer:-}$

Given :-

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♦Angles of Quadrilateral

• 5x

• 3x + 10

• 6x- 20

• x + 25

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To find :-

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♦ Value of x

♦ Measure or each angle of the Quadrilateral

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Solution :-

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Angle addition postulate :-

Sum refers to addition, so we will add all the given value of the angles. Let's begin.

$5x + 3x + 10 + 6x - 20 + x + 25 = 360$

Bring all the numbers and x together ,

$8x + 6x + x + 10 - 20 + 25 = 360$

$14 + x - 10 + 25 = 360$

$15x + 15 = 360$

$15x = 360 - 15$

$15x = 345$

$x = \frac{345}{15}$

Dividing LHS by 15 ,

$x = 23$

$hence \: value \: of \: x = 23$

♦ Substitute the value of x in the values of angles given in question.

1. 5x = 5 × 23 = 115 °

2. 3x + 10 = 3 × 23 + 10 = 69 + 10 = 79°

3. 6x - 20 = 6 × 23 - 20 = 138 - 20 = 118°

4. x + 25 = 23 + 25 = 48°

We found the value of x as well as all the angles. Let's verify the answer.

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$\huge \brown {Verification}$

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If we get the sum of all the values of the angles of quadrilateral equal to 360° then our answer is right.

So , let's check...

$= > 115 + 79 + 118 + 48 = 360 \\ = > 194 + 118 + 48 = 360 \\ = > 194 + 116 = 360 \\ = > 360 = 360$

:. LHS = RHS

Hence, our answer is right.✓