If, in the quadrilateral JKLM, the measures of the angles J, K, L, and M are in the ratio 2 : 3 : 5 : 6, then the quadrilateral is a:
Trapezium
The correct answer is Option 1 i.e. Trapezium.
J : K : L : M = 2 : 3 : 5 : 6
The sum of these angles
⇒ 2x + 3x + 5x + 6x = 360
⇒ 16x = 360
⇒ x = 22.5
So,
⇒ J = 2x = 45°
⇒ K = 3x = 67.5°
⇒ L = 5x = 112.5°
⇒ M = 6x = 135°
In a trapezium (or trapezoid), one pair of opposite sides is parallel. This condition is met when the sum of adjacent angles on the same side adds up to 180°.
Here, angles J and M (on one side) sum to: 45 + 135 = 180°
So, quadrilateral JKLM satisfies the condition of a trapezium
Similar Questions
- A quadrilateral with equal sides, whose angles are NOT right angles, is known as:
Important Questions from Quadrilaterals
The area of a rectangle is 300 cm 2and the length of its diagonal is 25 cm. The perimeter of the rectangle (in cm) is:
The adjacent angles of a rhombus are in the ratio of 3 : 6. The smallest angle of the rhombus is:
The area of a trapezium is 18 sq.cm. Its height and base are 3 cm and 5 cm respectively. Find the length of the side parallel to the base.
Find the area of a rhombus whose perimeter is 116 cm and one diagonal is 42 cm in length.
The ratio of sides to a quadrilateral is 2 ∶ 3 ∶ 4 ∶ 5 and the perimeter is 560 cm. Find out the smallest side. (In cm)
