Question

the angles of a quadrilateral are (5x) , (3x+10) , (6x-20) and (x+25) . find (1)the value of x and (2)the measure of each of the angle of the quadrilateral.

Answer 1

Answer:

Step-by-step explanation:

Sum of angles of a quadilateral is 360  

5x+3x+10+6x-20+x+25=360  

 

15x+15=360 360

15x=360-15=345 345

x=345/15 23

x=23  

The angles are:  

5x= 5*23=115 115

3x+10= (3*23)+10=79 79

6x-20=(6*23)-20+118 118

x+25=23+25=48 48

Answer 2

$\bf{\huge{\underline{\boxed{\rm{\blue{Answer:}}}}}}$

Gívéń :-

• Angles of a Quadrilateral

1. 5x
2. 3x + 10
3. 6x - 20
4. x + 25

Tó Fíńd :-

• Value of x
• The measure of each of the angle of the quadrilateral.

Solution :-

Angle addition postulate :-

• Sum of measures of all angles of a quadrilateral is 360°

Sum refers too 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 numbers and x together,

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

14x + x - 10 + 25 = 360

15x + 15 = 360

15x = 360 - 15

15x = 345

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

Dividing LHS by 15,

x = 23

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.

$\bf{\huge{\underline{\boxed{\rm{\red{Verification:}}}}}}$

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

Let's begin!

$\bf\implies$ 115 + 79 + 118 + 48 = 360

$\bf\implies$ 194 + 118 + 48 = 360

$\bf\implies$ 194 + 166 = 360

$\bf\implies$ 360 = 360

LHS = RHS.

Hence our answer is right.