Advertisements
Advertisements
Question
In a parallelogram ABCD, if ∠DAB = 75° and ∠DBC = 60°, then ∠BDC =
Options
75°
60°
45°
55°
Advertisements
Solution
Parallelogram can be drawn as :
We know that the opposite angles of a parallelogram are equal.
Therefore, ∠DCB = ∠DAC
∠DBC = 75°
By angle sum property of a triangle:
∠DBC + ∠DCB + ∠BDC = 180°
60° + 75 + ∠BCD = 180°
135° + ∠BDC = 180°
∠BDC = 180°-135°
∠BDC = 45°
Thus, ∠BDC measures 45°.
Hence the correct choice is (c).
APPEARS IN
RELATED QUESTIONS
Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.
The following statement are true and false .
In a parallelogram, the diagonals are equal
The following statement are true and false .
In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram.
The following statement are true and false .
If all the sides of a quadrilateral are equal it is a parallelogram.
If ABCD is a rhombus with ∠ABC = 56°, find the measure of ∠ACD.
In the given figure, ABCD and AEFG are two parallelograms. If ∠C = 58°, find ∠F.
Complete the following statement by means of one of those given in brackets against each:
If one angle of a parallelogram is a right angle, then it is necessarily a .................
The diagonals of a parallelogram ABCD intersect at O. If ∠BOC = 90° and ∠BDC = 50°, then ∠OAB =
ABCD is a parallelogram and E is the mid-point of BC. DE and AB when produced meet at F. Then, AF =
