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Answer:
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Answer:
1) Let the angles be 2x, 3x, 3x, 4x.
Sum of all angles of a quadrilateral = 360°
2x + 3x + 3x + 4x = 360°
12x = 360°
x = 30°
2x = 2*30° = 60°
3x = 3*30° = 90°
3x = 3*30° = 90°
4x = 4*30° = 120°
2) Opposite angles of a Parallelogram are equal
∠1 = ∠3
(5x-2)° = (40-x)°
5x + x = 40° + 2°
6x = 42°
x = 7°
(5x-2)° = (5*7 -2)° = 33°
(40-x)° = (40-7)° = 33°
Let the ∠2 be x.
As opposite side of a Parallelogram are equal
∠2 = ∠4
x = ∠4
Sum of all angles of a parallelogram = 360°
∠1 + ∠2 + ∠3 + ∠4 = 360°
33° + 33° + x + x = 360°
2x = 360° - 66°
2x = 294°
x = 147°
All angles are 33°, 33°, 147°, 147°.
3) Let the interior angle be x
Then According to the question :
Exterior angle = (2/3)x
Now, Sum of interior and exterior angles = 180
Therefore: x+(2/3)x=180
⇒ (5/3)x = 180
⇒ x = 108
Assuming that the polygon has n sides then;
Angle sum property ⇒ Total interior angle= 108*n....................[1 ]
Total no. of Interior angle = (n-2)*180.....................[2]
Equating [1 ] and [2] ,
108*n = (n-2)180
108*n = 180*n - 360
180*n - 108*n = 360
72*n = 360
n= 360/72
n=5
Therefore, It is a 5 sided regular ploygon rather say a Pentagon.
4) Question 5 is not visible properly. The last line is not visible in it.
Hope it helps!
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