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प्रश्न
Measure of one angle of a rhombus is 50°, find the measures of remaining three angles.
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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
ABCD is a parallelogram in which ∠A = 70°. Compute ∠B, ∠C and ∠D.
In the following Figure ABCD is a arallelogram, CE bisects ∠C and AF bisects ∠A. In each of the following, if the statement is true, give a reason for the same:
(i) ∠A = ∠C
(ii) \[\angle FAB = \frac{1}{2}\angle A\]
(iii) \[\angle DCE = \frac{1}{2}\angle C\]
(iv) \[\angle CEB = \angle FAB\]
(v) CE || AF
Which of the following statement is true for a rhombus?
It has only two pairs of equal sides.
Construct a rhombus whose diagonals are of length 10 cm and 6 cm.
ABCD is a rhombus whose diagonals intersect at O. If AB = 10 cm, diagonal BD = 16 cm, find the length of diagonal AC.
State with reason whether the following statement is ‘true’ or ‘false’.
Every rhombus is a rectangle.
Lengths of diagonals of a rhombus ABCD are 16 cm and 12 cm. Find the side and perimeter of the rhombus.
A quadrilateral whose all sides are equal, opposite angles are equal and the diagonals bisect each other at right angles is a ______.
In a rhombus diagonals intersect at ______ angles.
ABCD is a rhombus such that the perpendicular bisector of AB passes through D. Find the angles of the rhombus.
Hint: Join BD. Then ∆ABD is equilateral.
