Advertisements
Advertisements
प्रश्न
Use the information given in the following figure to find :
(i) x
(ii) ∠B and ∠C
Advertisements
उत्तर
∵ ∠A = 90° (Given)
∠B = (2x + 4°)
∠C = (3x - 5°)
∠D = (8x - 15°)
∠A + ∠B + ∠C + ∠D = 360°
90° + (2x + 4°) + (3x - 5°) + (8x - 15°) = 360°
90° + 2x + 4° + 3x - 5° + 8x - 15° = 360°
⇒ 74° + 13x = 360°
⇒ 13x = 360° - 74°
⇒ 13x = 286°
⇒ `x = 286/13`
⇒ x = 22°
∵ ∠B = 2x 4 = 2 × 22° + 4 = 48°
∠C = 3x - 5 = 3 × 22° - 5 = 61°
Hence (i) 22° (ii) ∠B = 48°, ∠C = 61°
संबंधित प्रश्न
Complete of the following, so as to make a true statement:
A quadrilateral has ...... angles.
Complete of the following, so as to make a true statement:
A quadrilateral has .... diagonals.
Complete of the following, so as to make a true statement:
A point is in the interior of a convex quadrilateral, if it is in the ..... of its two opposite angles.
In Fig. 16.19, ABCD is a quadrilateral.
Name a pair of opposite angles.
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.
ABCD is a trapezium in which AB || DC. M and N are the mid-points of AD and the respectively. If AB = 12 cm, MN = 14 cm, then CD =
Use the information given in the following figure to find the value of x.
Two diagonals of an isosceles trapezium are x cm and (3x – 8) cm. Find the value of x.
Angle A of an isosceles trapezium ABCD is 115°; find the angles B, C and D.
In parallelogram ABCD, ∠A = 90°
(i) What is the measure of angle B.
(ii) Write the special name of the parallelogram.
Observe the figure below and find out their name.
The angles of a pentagon are x°, (x - 10)°, (x + 20)°, (2x - 44)° and (2x - 70)°. Find the angles.
One angle of a hexagon is 140° and the remaining angles are in the ratio 4 : 3 : 4 : 5 : 4. Calculate the measures of the smallest and the largest angles.
If the sum of two angles is greater than 180°, then which of the following is not possible for the two angles?
In the following figure,
∠AOD is a/an ______ angle
In the following figure, What is BD – BE?
What conclusion can be drawn from part of given figure, if DB is the bisector of ∠ADC?
What conclusion can be drawn from part of given figure, if BD bisects ∠ABC?
Investigate :
Use strips and fasteners to make a triangle and a quadrilateral.
Try to push inward at any one vertex of the triangle. Do the same to the quadrilateral. Is the triangle distorted? Is the quadrilateral distorted? Is the triangle rigid?
Why is it that structures like electric towers make use of triangular shapes and not quadrilaterals?
