Question

Find the measurement of the biggest and the smallest in the adjacent figure. ​

Answer 1

Answer: sum of all the angles =360

hence,

(5x-30)+(2x+30)+(3x-70)+(3x+40)=360

5x-30+2x+30+3x-70+3x+40=360

(5x+2x+3x+3x)+(-30+30-70+40)=360

13x-30=360

13x=360+30

x=390/13

x=30

therefore,

angle 1=2x+30=60+30=90

angle 2=3x-70=90-70=20

angle 3=3x+40=90+40=130

angle 4=5x-30=150-30=120

therefore biggest angle is 130 and smallest is 20

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Answer 2

Answer :

Given :

• All the angles of a complete angle are given. That are :
• Angle 1 = (2x + 30)°
• Angle 2 = (3x - 70)°
• Angle 3 = (3x + 40)°
• Angle 4 = (5x - 30)°

Find :

• The measurement of the biggest and the smallest in the adjacent figure.

$\large{\mathfrak{\underline{Solution:-}}}$

Here, we have all the angles of a complete angle and we need to find the measurement of the biggest and smallest angle of the adjacent figure.

We know that,

• The sum of all the angles of a complete angle is 360°.

As,

We already have all the angles , so put there sum equal to 360°

$\dag$ Putting values equal to 360°

$\rightarrow$ (2x + 30) + (3x - 70) + (3x + 40) + ( 5x - 30 ) = 360°

$\rightarrow$ (5x - 40) + (8x + 10) = 360°

$\rightarrow$ (13x - 30) = 360°

$\rightarrow$ 13x = 360 + 30

$\rightarrow$ 13x = 390

$\rightarrow$ x = ${\sf{\cancel{\dfrac{ 390 }{13}}}}$

$\rightarrow$ x = 30°

From here,

We have the value of x is equal to 30°

Now, let us find the measurement of biggest and smallest angles

» Put the x = 30° in all of the following angles one by one :-

Angle 1 = (2x + 30)°

• = 2(30) + 30
• = 60 + 30
• = 90°

Angle 2 = (3x - 70)°

• = 3(30) - 70
• = 90 - 70
• = 20°

Angle 3 = (3x + 40)°

• = 3(30) + 40
• = 90 + 40
• = 130°

Angle 4 = (5x - 30)°

• = 5(30) - 30
• = 150 - 30
• = 120°

From above, we have calculated the biggest and smallest angles that are :-

➡Angle 3 is the greatest angle that is of 130°

➡Angle 2 is the smallest angle that is of 20°

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