In quadrilateral PQRS, \(\angle P = 2\angle Q,\ \angle Q = \dfrac{\angle R}{4},\ \angle R = 2\angle S\). Find the value of \(\angle S\).
80°
Let \(\angle S = x\). Then \(\angle R = 2x\), \(\angle Q = \tfrac{\angle R}{4} = \tfrac{x}{2}\), and \(\angle P = 2\angle Q = x\).
Sum of angles in a quadrilateral: \(\angle P+\angle Q+\angle R+\angle S = 360^\circ\).
\(x+\tfrac{x}{2}+2x+x = 4.5x = 360 \Rightarrow x=80\).
Hence, the value of \(\angle S\) is 80°.
Similar Questions
- If one angle of a parallelogram is $18^\circ$ less than twice the smallest angle of the same parallelogram, then the largest angle of the parallelogram is:
- Find the area of a trapezium whose parallel sides are 10 cm and 20 cm and non-parallel sides are equal to 10 cm.
- The angles of a quadrilateral are in the ratios 2 : 4 : 6 : 8. The smallest of these angles is:
- The angles of a quadrilateral are in the ratio of 1 : 3 : 4 : 7. What is the difference between the largest and the smallest angle?
- If ABCD is a cyclic quadrilateral and ABC is an equilateral triangle find the angle of CDA.
- If one angle of a parallelogram is $39^\circ$ less than twice the smallest angle, then the smallest angle of the parallelogram is:
- If one angle of a parallelogram is $30^\circ$ less than twice the measure of the smallest angle, then the measure of the largest angle of the parallelogram is:
- In a rhombus ABCD, if $\angle ACB = 40^\circ, \text{then } \angle ADB = ?$
- P is the mid-point of side BC of a parallelogram ABCD such that $\angle BAP = \angle DAP$.
If AD = 10 cm, then CD = ? - If the angles of a quadrilateral are in the ratio of 4 : 9 : 11 : 12, then the largest of these angles is:
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)
