Q. 34.3( 3 Votes )

# In the given figure, ABCD is a parallelogram in which ∠BAD = 75° and ∠CBD = 60°. Then, ∠BDC = ?

A. 60^{o}

B. 75^{o}

C. 45^{o}

D. 50^{o}

Answer :

It is given in the question that,

In parallelogram ABCD: ∠ BAD = 75^{o}, ∠ CBD = 60^{o}

Now, ∠ DAB = ∠ DCB = 75^{o} (Opposite angles)

Also, in triangle DBC we know that sum of angles of a triangle is 180^{o}

∠ DBC + ∠ BDC + ∠ DCB = 180^{o}

60^{o} + ∠ BDC + 75^{o} = 180^{o}

135^{o} + ∠ BDC = 180^{o}

∠ BDC = 180^{o} – 135^{o}

∠ BDC = 45^{o}

Hence, option (C) is correct

Rate this question :

If the diagonals of a rhombus are 18 cm and 24 cm respectively, then its side is equal to

RD Sharma - MathematicsIn a parallelogram ABCD, if ∠DAB=75° and ∠DBC=60°, then ∠BDC=

RD Sharma - MathematicsThe diagonals AC and BD of a rectangle ABCD intersect each other at P. If ∠ABD =50°, then ∠DPC =

RD Sharma - MathematicsIn a quadrilateral ABCD, ∠A+∠C is 2 times ∠B+∠D. If ∠A= 140° and f∠D = 60°, then ∠B=

RD Sharma - MathematicsIf one side of a parallelogram is 24° less than twice the smallest angle, then the measure of the largest angle of the parallelogram is

RD Sharma - MathematicsIf the degree measures of the angles of quadrilateral are 4x, 7x, 9x and 10x, what is the sum of the measures of the smallest angle and largest angle?

RD Sharma - MathematicsIf an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is

RD Sharma - MathematicsIn Fig. 14.112, ABCD is a trapezium. Find the values of x and y.

RD Sharma - Mathematics