Three angles of a quadrilateral are in the ratio 2:3:4. The sum of the least and the greatest of these three angles is equal to 180 degree.Find all the angles of this quadrilateral.
Answers
Step-by-step explanation:
let the angle be 2x, 3x ,and 4x
A.T.Q.
the greatest angle + the least angle is = 180
4x + 2x = 180
6x. = 180
x. = 30
so the angle are 2×30= 60
3×30. =90
4× 30 =. 120
Let fourth angle be K
now all the four angle sum of quadrilateral is 360
therefore
60+120+90+k. = 360
k =90
so all four angle are 90, 60. 120.,90
The fourth angles of quadrilateral is 90°.
Explanation:
Given: Three angles of a quadrilateral are in the ratio = 2 : 3 : 4
The sum of the least and the greatest of these three angles is equal to 180°.
Assume the angles be 2x, 3x and 4x.
The greatest angle is 4x and the least is 2x.
According to the question,
4x + 2x = 180
⇒ 6x = 180
⇒ x = 180 ÷ 6
⇒ x = 30
Hence, the three angles of quadrilateral are
2 × 30 = 60°
3 × 30° = 90° and
4 × 30° = 120°.
Fourth angle of quadrilateral = 360° – 60° + 90° + 120° ⇒ 360° – 270° = 90°
The fourth angles of quadrilateral is 90°.
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