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प्रश्न
ABCD is a rhombus. If ∠ACB = 40°, find ∠ADB.
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उत्तर
\[\text{ In a rhombus, the diagonals are perpendicular } . \]
\[ \therefore \angle BPC = 90°\]
\[\text{ From ∆ BPC, the sum of angles is }180° . \]
\[ \therefore \angle CBP + \angle BPC + \angle PBC = 180°\]
\[\angle CBP = 180° - \angle BPC - \angle PBC\]
\[\angle CBP = 180° - 40° - 90° = 50° \]
\[\angle ADB = \angle CBP = 50°(\text{ alternate angle })\]
संबंधित प्रश्न
Name the quadrilaterals whose diagonals are perpendicular bisectors of each other
If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
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
Draw a rhombus, having each side of length 3.5 cm and one of the angles as 40°.
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(i) Is ∆BOC ≅ ∆DOC? State the congruence condition used?
(ii) Also state, if ∠BCO = ∠DCO.
Identify all the quadrilateral that have Four sides of equal length
Diagonals of a parallelogram intersect each other at point O. If AO = 5, BO = 12 and AB = 13 then show that `square`ABCD is a rhombus.
State with reason whether the following statement is ‘true’ or ‘false’.
Every rhombus is a rectangle.
In rhombus ABCD;
(i) if ∠A = 74° ; find ∠B and ∠C.
(ii) if AD = 7.5 cm ; find BC and CD.
In a rhombus diagonals intersect at ______ angles.
