Advertisements
Advertisements
Question
In a parallelogram ABCD, ∠D = 135°, determine the measures of ∠A and ∠B
Solution
In a parallelogram ABCD
Adjacent angles are supplementary
So, `∠`D + `∠`C =180°
135° + `∠`C =180° ⇒ `∠`C =180° -135°
`∠`C = 45°
In a parallelogram opposite sides are equal
`∠`A = ÐC = 45°
`∠`B = ÐD = 135°
APPEARS IN
RELATED QUESTIONS
In ΔABC and ΔDEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see the given figure). Show that
(i) Quadrilateral ABED is a parallelogram
(ii) Quadrilateral BEFC is a parallelogram
(iii) AD || CF and AD = CF
(iv) Quadrilateral ACFD is a parallelogram
(v) AC = DF
(vi) ΔABC ≅ ΔDEF.
The following statement are true and false.
In a parallelogram, the diagonals bisect each other.
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.
The perimeter of a parallelogram is 22 cm. If the longer side measures 6.5 cm, what is the measure of shorter side?
Complete the following statement by means of one of those given in brackets against each:
Consecutive angles of a parallelogram are ...................
PQRS is a quadrilateral, PR and QS intersect each other at O. In which of the following case, PQRS is a parallelogram?
PQ = 7 cm, QR = 7 cm, RS = 8 cm, SP = 8 cm
PQRS is a quadrilateral, PR and QS intersect each other at O. In which of the following case, PQRS is a parallelogram?
OP = 6.5 cm, OQ = 6.5 cm, OR = 5.2 cm, OS = 5.2 cm
In a parallelogram ABCD, if ∠DAB = 75° and ∠DBC = 60°, then ∠BDC =
ABCD is a parallelogram, M is the mid-point of BD and BM bisects ∠B. Then ∠AMB =
