Question

The four angles of a quadrilateral are in the ratio 3:4:5:6 find the angles

Answer 1

DEAR STUDENT,
THIS IS YOUR ANSWER.....
Ratio of angles of quadrilateral is 3:4:5:6.
Let the angles of quadrilateral be 3x,4x,5x,6x
As we know that sum of all angles of a quadrilateral= 360°
So , ACC. TO QUESTION
3x+4x+5x+6x=360°
18x= 360°
x=360/18
x=20°
So The value of x = 20°
Therefore the angles of quadrilateral -->
1st angle= 3x=3×20°=60°
2nd angle=4x=4×20°=80°
3rd angle=5x=5×20°=100°
4th angle= 6x= 6×20°=120°
Hence, the angles of a quadrilateral are 60°, 80°, 100° and 120°.
HOPE IT HELPS.......^_^
PLZZZ MARK AS BRAINLIEST.....^_^

Answer 2

Solution:

$\text{Given ratio of 4 angles = 3:4:5:6}\\\\\text{Let each angle be 3x, 4x, 5x and 6x.}\\\\\text{We know that the sum of the 4 interior angles of any quadrilateral is 360}^{\circ}.\\\\\text{Thus, } 3x+4x+5x+6x = 360\\\\\implies 18x = 360\\\\\implies x = 360 \div 18 = \boxed{20}\\\\\therefore \: \text{The angles are 3(20) = 60 ^{\circ} , 4(20) = 80 ^{\circ} , 5(20) = 100 ^{\circ} and 6(20) = 120 ^{\circ} .}\\\\\text{The answers can be verified by adding all the angles. If the sum is 360,}$

$\text{then its correct or else, its wrong.}\\\\\text{Adding the angles, we get 60 + 80 + 100 + 120 = 360 ^{\circ} }\\\\\text{Hence, the answer is correct.}$

Thanks!