If the angels of a quadrilateral are in the ratio 5:8:11:12, find all the angels.
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Answered by
1
Ratio of angle of quadrilateral = 5: 8: 11:12
Let angle be 5x, 8x, 11x, 12x
So, by angle sum property
5x + 8x + 11x + 12x = 360
Or 36x = 360
Or x = 360 / 36
X = 10
Fisrt angle = 5* 10= 50
Second angle= 8*10 = 80
Third angle = 11*10 = 110
Fourt angle = 12*10 =120
Angle be 50, 80, 110, 120
Let angle be 5x, 8x, 11x, 12x
So, by angle sum property
5x + 8x + 11x + 12x = 360
Or 36x = 360
Or x = 360 / 36
X = 10
Fisrt angle = 5* 10= 50
Second angle= 8*10 = 80
Third angle = 11*10 = 110
Fourt angle = 12*10 =120
Angle be 50, 80, 110, 120
Answered by
7
Answer :-
- Angles are 50°, 80°, 110° and 120°.
Given :-
- The angles of a quadrilateral are in the ratio 5 : 8 : 11 : 12.
To Find :-
- Those angles.
Solution :-
Put x in the ratio
Now angles are
- 5x
- 8x
- 11x
- 12x
As we know that
- Sum of all angles of a quadrilateral is 360°.
According to question :-
⇒ 5x + 8x + 11x + 12x = 360°
⇒ 13x + 11x + 12x = 360°
⇒ 13x + 23x = 360°
⇒ 36x = 360°
⇒ x = 360/36
⇒ x = 10
Put the value of x in the ratio
- 5x = 5 × 10 = 50°
- 8x = 8 × 10 = 80°
- 11x = 11 × 10 = 110°
- 12x = 12 × 10 = 120°
Verification :-
⇒ 5x + 8x + 11x + 12x = 360°
⇒ 50° + 80° + 110° + 120° = 360°
⇒ 130° + 230° = 360°
⇒ 360° = 360°
Hence, verified !
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