Advertisements
Advertisements
प्रश्न
The angles P, Q, R and S of a quadrilateral are in the ratio 1:3:7:9. Then PQRS is a ______.
पर्याय
parallelogram
trapezium with PQ || RS
trapezium with QR || PS
kite
Advertisements
उत्तर
The angles P, Q, R and S of a quadrilateral are in the ratio 1:3:7:9. Then PQRS is a trapezium with PQ || RS.
Explanation:
Let the angles be x, 3x, 7x and 9x, then
x + 3x + 7x + 9x = 360° ...[∵ Sum of angles in any quadrilateral is 360°]
⇒ 20x = 360°
⇒ x = `360^circ/20`
⇒ x = 18°
Then, the angles P, Q, R and S are 18°, 54°, 126° and 162°, respectively.
Since, ∠P + ∠S = 18° + 162° = 180° and ∠Q + ∠R = 54° + 126° = 180°
∴ The quadrilateral PQRS is a trapezium with PQ || RS.
APPEARS IN
संबंधित प्रश्न
Find the angle measure x in the given Figure
Find the angle measure x in the given Figure
PQRS is a square such that PR and SQ intersect at O. State the measure of ∠POQ.
If PQRS is a square, then write the measure of ∠SRP.
If the angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13, then find the measure of the smallest angle.
In the given figure, PQRS is a rhombus in which the diagonal PR is produced to T. If ∠SRT = 152°, find x, y and z.
Can the angles 110º, 80º, 70º and 95º be the angles of a quadrilateral? Why or why not?
Which of the following can be four interior angles of a quadrilateral?
The polygon in which sum of all exterior angles is equal to the sum of interior angles is called ______.
In a quadrilateral PQRS, ∠P = 50°, ∠Q = 50°, ∠R = 60°. Find ∠S. Is this quadrilateral convex or concave?
