Advertisements
Advertisements
प्रश्न
The diagonals of a rectangle ABCD meet at O, If ∠BOC = 44°, find ∠OAD.
Advertisements
उत्तर
The rectangle ABCD is given as:
We have,
∠BOC +∠BOA = 180° (Linear pair)
44° +∠BOA = 180°
∠BOA = 180° -44°
∠BOA = 136°
Since, diagonals of a rectangle are equal and they bisect each other. Therefore, in ΔOAB, we have
OA = OB (Angles opposite to equal sides are equal.)
Therefore,
∠1 = ∠2
Now,in ΔOAB, we have
∠BOA + ∠1 +∠2 = 180
∠BOA + 2∠1 = 180°
2∠1 = 44°
∠1 = 22°
Since, each angle of a rectangle is a right angle.
Therefore,
∠BAD = 90°
∠1+∠3 = 90°
22° +∠3 = 90°
∠3 = 68°
Thus, ∠OAD = 68°
Hence, the measure of∠OAD is 68°.
APPEARS IN
संबंधित प्रश्न
Find the angle measure x in the given Figure
Find x + y + z + w
The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13 Find all the angles of the quadrilateral.
In Fig. below, ABCD is a parallelogram in which ∠DAB = 75° and ∠DBC = 60°. Compute
∠CDB and ∠ADB.
If PQRS is a square, then write the measure of ∠SRP.
If the angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13, then find the measure of the smallest angle.
Can all the angles of a quadrilateral be right angles? Give reason for your answer.
One angle of a quadrilateral is of 108º and the remaining three angles are equal. Find each of the three equal angles.
If three angles of a quadrilateral are each equal to 75°, the fourth angle is ______.
Three angles of a quadrilateral are equal. Fourth angle is of measure 120°. What is the measure of equal angles?
