Advertisements
Advertisements
प्रश्न
Measure of one angle of a rhombus is 50°, find the measures of remaining three angles.
Advertisements
उत्तर
Suppose ABCD is a rhombus.
Let m∠A = 50º
Opposite angles of a rhombus are congruentes.
∴ m∠C = m∠A = 50º and m∠B = m∠D
Now,
m∠A + m∠B + m∠C + m∠D = 360º
∴ 50º + m∠B + 50º + m∠D = 360º
⇒ m∠B + m∠D = 360º − 100º = 260º
⇒ 2 m∠B = 260º ...(m∠B = m∠D)
⇒ m∠B = `(260°)/2` = 130°
∴ m∠D = m∠B = 130º
Thus, the measures of the remaining angles of the rhombus are 130º, 50º, and 130º.
संबंधित प्रश्न
The following figure is parallelogram. Find the degree values of the unknown x, y, z.
In the following figure RISK and CLUE are parallelograms. Find the measure of x.
Diagonals of parallelogram ABCD intersect at O as shown in the following fegure. XY contains O, and X, Y are points on opposite sides of the parallelogram. Give reasons for each of the following:
(i) OB = OD
(ii) ∠OBY = ∠ODX
(iii) ∠BOY = ∠DOX
(iv) ∆BOY ≅ ∆DOX
Now, state if XY is bisected at O.
Fill in the blank, in each of the following, so as to make the statement true:
If the diagonals of a parallelogram bisect each other at right angles, then it is a ......
The diagonals of a parallelogram are not perpendicular. Is it a rhombus? Why or why not?
If the diagonals of a rhombus are 12 cm and 16cm, find the length of each side.
Draw a rhombus ABCD, if AB = 6 cm and AC = 5 cm.
ABCD is a rhombus and its diagonals intersect at O.
(i) Is ∆BOC ≅ ∆DOC? State the congruence condition used?
(ii) Also state, if ∠BCO = ∠DCO.
If opposite angles of a rhombus are (2x)° and (3x - 40)° then value of x is ______.
Diagonals PR and QS of a rhombus PQRS are 20 cm and 48 cm respectively. Find the length of side PQ.
