Advertisements
Advertisements
Question
Can a quadrilateral ABCD be a parallelogram if ∠A = 70° and ∠C = 65°?
Advertisements
Solution
No, because in a parallelogram opposite angles are equal but here ∠A ≠ ∠C.
APPEARS IN
RELATED QUESTIONS
In the given figure, `square`PQRS and `square`ABCR are two parallelograms. If ∠P = 110° then find the measures of all angles of `square`ABCR.

In the given figure, if points P, Q, R, S are on the sides of parallelogram such that AP = BQ = CR = DS then prove that `square`PQRS is a parallelogram.

Construct ☐ BARC such that l(BA) = l(BC) = 4.2 cm, l(AC) = 6.0 cm, l(AR) = l(CR) = 5.6 cm
In parallelogram ABCD, ∠A = 3 times ∠B. Find all the angles of the parallelogram. In the same parallelogram, if AB = 5x – 7 and CD = 3x +1 ; find the length of CD.
Prove that the diagonals of a parallelogram bisect each other.
In parallelogram ABCD, X and Y are midpoints of opposite sides AB and DC respectively. Prove that:
(i) AX = YC
(ii) AX is parallel to YC
(iii) AXCY is a parallelogram.
The given figure shows parallelogram ABCD. Points M and N lie in diagonal BD such that DM = BN.

Prove that:
(i) ∆DMC = ∆BNA and so CM = AN
(ii) ∆AMD = ∆CNB and so AM CN
(iii) ANCM is a parallelogram.
If two adjacent angles of a parallelogram are (5x – 5)° and (10x + 35)°, then the ratio of these angles is ______.
In the given figure, ABCD and BDCE are parallelograms with common base DC. If BC ⊥ BD, then ∠BEC = ______.

Construct a parallelogram ABCD in which AB = 4 cm, BC = 5 cm and ∠B = 60°.
