Advertisements
Advertisements
Question
The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13 Find all the angles of the quadrilateral.
Advertisements
Solution
Let the common ratio between the angle is ‘ЁЭСе’ so the angles will be 3x, 5x, 9x and 13x
respectively
Since the sum of all interior angles of a quadrilateral is 360°
∴ 3x + 5x + 9x +13x = 360°
⇒ 30x = 360°
⇒ x =12°
Hence, the angles are
3x = 3 × 12 = 36°
5x = 5 × 12 = 60°
9x = 9 ×12 =108°
13x =13× 12 =156°
APPEARS IN
RELATED QUESTIONS
Find the angle measure x in the given Figure
Find x in the following figure:
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 a quadrilateral ABCD, bisectors of angles A and B intersect at O such that ∠AOB = 75°, then write the value of ∠C + ∠D.
In the given figure, ABCD is a rectangle in which diagonal AC is produced to E. If ∠ECD = 146°, find ∠AOB.
Can all the angles of a quadrilateral be acute angles? Give reason for your answer.
The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60º. Find the angles of the parallelogram.
A quadrilateral has three acute angles. If each measures 80°, then the measure of the fourth angle is ______.
The angles P, Q, R and S of a quadrilateral are in the ratio 1:3:7:9. Then PQRS is a ______.
