(ii) The angles of a quadrilateral are in ratio 2:5:7:10.Find the four angles
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The angles of a quadrilateral are in ratio 2:5:7:10 .Find the four angles
Here , the angles of a quadrilateral are in the ratio 2 : 5 : 7 : 10 .
To find -
Find all the four angles .
Solution -
The angles of a quadrilateral are in the ratio 2 : 5 : 7 : 10 .
Let the angles be 2x , 5x, 7x and 10x respectively .
Now , as the figure is a quadrilateral, all the angles add upto 360°.
So , we can formulate the following equation -
⇛2x + 5x + 7x + 10x = 360°
⇛ 24x = 360°
⇛x = 12°
Angle A = 2x = 2 × 12° = 24°
Angle B = 5x = 5 × 12° = 60°
Angle C = 7x = 7 × 12° = 84°
Angle D = 10x = 10 × 12° = 120°
The required angles of the quadrilateral are 24°, 60° , 84° and 120° respectively .
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Answer:
Question -
(ii) The angles of a quadrilateral are in ratio 2:5:7:10.Find the four angles
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Given -
Angles = 2,5,710
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To find -
The missing angles .
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Solution-
Let's first take the given angles as = 2x,5x,7x,10x
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Now, let's solve it further.
(reason- sum of all sides of a quadrilateral is 360°)
So,
x=15°
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Required Answer -
2x=2×x=2×15= 30°
5x=5×15=75°
7x= 7×105= 105°
10x= 10×15=150°