Question

find the biggest and smallest angle of the figure
plz solve it with full formula
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Answer 1

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ANSWER

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Largest angle = \angle3∠3 = 130°

Smallest angle = \angle2∠2 = 20°

Explanation :

From the figure, the sum of all angles = 360°

\angle∠ 1 + \angle∠ 2 + \angle∠ 3 + \angle∠ 4 = 360°

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

13x - 30 = 360°

13x = 390°

x = 390/ 13

x = 30°

Hence, the angles are

(2x + 30) = 90°

(3x - 70) = 20°

(3x + 40) = 130°

(5x - 30) = 120°

Therefore, largest angle = \angle 3∠3 = 130°

Smallest angle = \angle 2∠2 = 20

Answer 2

Answer:

sum of all angles here = 360°

angle 1st + angle 2nd + angle 3rd + angle 4th= 360°

first angle= 2x + 30

second angle = 3x - 70

third angle = 3x + 40

fourth angle = 5x - 30

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

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

(2+3+3+5) X + (30+40-70-30) = 360°

(5+8) X + (70-100) = 360°

13x - 30 = 360°

13x = 360+30

13x = 390

x = 390/13

X = 30°

first angle = 2x + 30

= 2×30+30

= 60+30

= 90

second angle = 3x -70

= 3×30-70

= 90-70

= 20°

third angle = 3x + 40

= 3× 30+40

= 90+40

= 130°

fourth angle= 5x - 30

= 5×30-30

= 150-30

= 120°

therefore the smallest angle is 20° and the largest angle is 130°