Advertisements
Advertisements
Question
Angles of a quadrilateral are (4x)°, 5(x+2)°, (7x – 20)° and 6(x+3)°. Find :
(i) the value of x.
(ii) each angle of the quadrilateral.
Advertisements
Solution
Angles of quadrilateral are,
(4x)°, 5(x+2)°, (7x – 20)° and 6(x+3)°
∴ 4x + 5(x + 2) + (7x - 20) + 6(x + 3) = 360°
4x + 5x + 10 + 7x - 20 + 6x + 18 = 360°
22x + 8 = 360°
22x = 360° - 8°
22x = 352°
x = 16°
Hence angles are,
(4x)° = (4 × 16)° = 64°
5(x + 2)° = 5(16 + 2)° = 90°
(7x - 20)° = (7 × 16 - 20)° = 92°
6(x + 3)° = 6(16 + 3) = 114°
RELATED QUESTIONS
The perimeter of a parallelogram is 22 cm . If the longer side measures 6.5 cm what is the measure of the shorter side?
Define the following term Convex Quadrilateral .
In a quadrilateral, define of the following Vertices .
In a quadrilateral, define of the following Angles .
Complete of the following, so as to make a true statement:
A quadrilateral has .... diagonals.
In Fig. 16.21, the bisectors of ∠A and ∠B meet at a point P. If ∠C = 100° and ∠D = 50°, find the measure of ∠APB.
The measure of angles of a hexagon are x°, (x − 5)°, (x − 5)°, (2x − 5)°, (2x − 5)°, (2x + 20)°. Find the value of x.
In the given figure, PQRS is an isosceles trapezium. Find x and y.
In the given figure, ABCD is a trapezium. Find the values of x and y.
In ΔABC, E is the mid-point of median AD such that BE produced meets AC at F. IF AC = 10.5 cm, then AF =
Two angles of a quadrilateral are 68° and 76°. If the other two angles are in the ratio 5 : 7; find the measure of each of them.
Two adjacent angles of a parallelogram are 70° and 110° respectively. Find the other two angles of it.
In the quadrilateral ABCD, AB = BC and AD = DC Measure of ∠BCD is
In the figure, PQRS and PTVS are two cyclic quadrilaterals, If ∠QRS = 100°, then ∠TVS =
Which of the following is not true for a parallelogram?
A pair of opposite sides of a trapezium are ______.
In the following figure, What is AC – EC?
Using the information given, name the right angles in part of figure:
AE ⊥ CE
Draw a rough sketch of a quadrilateral PQRS. Draw its diagonals. Name them. Is the meeting point of the diagonals in the interior or exterior of the quadrilateral?
