Advertisements
Advertisements
प्रश्न
ABCD is a rhombus. If ∠BAC = 38°, find :
(i) ∠ACB
(ii) ∠DAC
(iii) ∠ADC.
Advertisements
उत्तर
ABCD is Rhombus (Given)
AB = BC
∠BAC = ∠ACB (∠s opp. to equal sides)
But ∠BAC = 38° (Given)
∠ACB = 38°
In ∆ABC,
∠ABC + ∠BAC + ∠ACB = 180°
∠ABC + 38°+ 38° = 180°
∠ABC = 180° – 76° = 104°
But ∠ABC = ∠ADC (opp. ∠s of rhombus)
∠ADC = 104°
∠DAC = ∠DCA ( AD = CD)
∠DAC = `1/2` [180° - 104°]
∠DAC = `1/2 xx` 76° = 38°
Hence (i) ∠ACB = 38° (ii) ∠DAC = 38° (iii) ∠ADC = 104° Ans.
APPEARS IN
संबंधित प्रश्न
Can the following figure be parallelogram. Justify your answer.
In a parallelogram ABCD, ∠D = 135°, determine the measure of ∠A and ∠B.
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 is a quadrilateral.
Which of the following statement is true for a rhombus?
It can be a square.
Identify all the quadrilateral that have Four sides of equal length
Diagonals of a rhombus are 20 cm and 21 cm respectively, then find the side of rhombus and its perimeter.
If all pairs of adjacent sides of a quadrilateral are congruent then it is called ______.
A quadrilateral whose all sides are equal, opposite angles are equal and the diagonals bisect each other at right angles is a ______.
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.
