Advertisements
Advertisements
Question
Can a quadrilateral ABCD be a parallelogram if ∠D + ∠B = 180°?
Advertisements
Solution
For ∠D + ∠B = 180°, quadrilateral ABCD may or may not be a parallelogram. Along with this condition, the following conditions should also be fulfilled.
The sum of the measures of adjacent angles should be 180º.
Opposite angles should also be of same measures.
APPEARS IN
RELATED QUESTIONS
Consider the given parallelograms. Find the values of the unknowns x, y, z.

Name the quadrilaterals whose diagonals bisect each other
In the adjacent figure, if seg AB || seg PQ, seg AB ≅ seg PQ, seg AC || seg PR, seg AC ≅ seg PR then prove that, seg BC || seg QR and seg BC ≅ seg QR.

Referring the adjacent figure of a parallelogram, write the answer of questions given below.

(1) If l(WZ) = 4.5 cm then l(XY) = ?
(2) If l(YZ) = 8.2 cm then l(XW) = ?
(3) If l(OX) = 2.5 cm then l(OZ) = ?
(4) If l(WO) = 3.3 cm then l(WY) = ?
(5) If m∠WZY = 120° then m∠WXY = ? and m∠XWZ = ?
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.
Given: Parallelogram ABCD in which diagonals AC and BD intersect at M.
Prove: M is the mid-point of LN.
ABCD is a parallelogram. What kind of quadrilateral is it if: AC is perpendicular to BD but is not equal to it?
Use the information given in the alongside diagram to find the value of x, y, and z.

The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30°. The measure of the obtuse angle is ______.
If opposite angles of a quadrilateral are equal, it must be a parallelogram.
