Advertisements
Advertisements
प्रश्न
Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C – 8° ; ∠A = 5(a+2)° and ∠B = 2(2a+7)°.
Calculate ∠A.
Advertisements
उत्तर
∵ ∠C = 64° (Given)
∴ ∠D = ∠C – 8° = 64°- 8° = 56°
∠A = 5(a+2)°
∠B = 2(2a+7)°
Now ∠A + ∠B + ∠C + ∠D = 360°
5(a+2)° + 2(2a+7)° + 64° + 56° = 360°
5a + 10 + 4a + 14° + 64° + 56° = 360°
9a + 144° = 360°
9a = 360° – 144°
9a = 216°
a = 24°
∴ ∠A = 5 (a + 2) = 5(24+2) = 130°
संबंधित प्रश्न
In Fig. 16.19, ABCD is a quadrilateral.
Name a pair of opposite angles.
In Fig. 16.19, ABCD is a quadrilateral.
How many pairs of adjacent angles are there?
Two angles of a quadrilateral are of measure 65° and the other two angles are equal. What is the measure of each of these two angles?
The consecutive sides of a quadrilateral have
Two angles of a quadrilateral are 89° and 113°. If the other two angles are equal; find the equal angles.
In a trapezium ABCD, side AB is parallel to side DC. If ∠A = x° and ∠D = (3x – 20)°; find the value of x.
Two opposite angles of a parallelogram are 100° each. Find each of the other two opposite angles.
In parallelogram ABCD, its diagonals intersect at point O. If OA = 6 cm and OB = 7.5 cm, find the length of AC and BD.
One angle of a pentagon is 160° and the rest are all equal angles. Find the measure of the equal angles.
ABCDE is a pentagon in which AB is parallel to DC and ∠A : ∠E : ∠D = 1 : 2 : 3. Find angle A.
If one angle of a cyclic quadrilateral is 75°, then the opposite angle is
A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is ______.
ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is ______.
D and E are the mid-points of the sides AB and AC respectively of ∆ABC. DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is ______.
A quadrilateral can be drawn when all the four angles and one side is given.
Using the information given, name the right angles in part of figure:
AC ⊥ BD
Using the information given, name the right angles in part of figure:
RS ⊥ RW
How many points are required to form a quadrilateral?
