Advertisements
Advertisements
Question
The diagonals of a rectangle ABCD meet at O, If ∠BOC = 44°, find ∠OAD.
Advertisements
Solution
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
RELATED QUESTIONS
Find the angle measure x in the given Figure
Find x + y + z + w
Find x in the following figure:
In Fig. below, ABCD is a parallelogram in which ∠DAB = 75° and ∠DBC = 60°. Compute
∠CDB and ∠ADB.
Diagonals necessarily bisect opposite angles in a
If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is
Can all the angles of a quadrilateral be acute angles? Give reason for your answer.
Can all the angles of a quadrilateral be right angles? Give reason for your answer.
The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60º. Find the angles of the parallelogram.
In the following figure, P is the mid-point of side BC of a parallelogram ABCD such that ∠BAP = ∠DAP. Prove that AD = 2CD.
