Advertisements
Advertisements
प्रश्न
If measures opposite angles of a parallelogram are (60 − x)° and (3x − 4)°, then find the measures of angles of the parallelogram.
उत्तर
Let ABCD be a parallelogram, with ∠A = (60 - x )° and∠C = (3x - 4).
We know that in a parallelogram, the opposite angles are equal.
Therefore,
∠A = ∠C
60 - x = 3x - 4
-x 3x = - 4 - 60
-4x = -64
x = 16
Thus, the given angles become
∠A = (60 - x)°
= (60 - 16)°
= 44 °
Similarly,
∠C = 44°
Also, adjacent angles in a parallelogram form the consecutive interior angles of parallel lines, which must be supplementary.
Therefore,
∠A +∠B = 180°
44° + ∠B = 180°
∠B = 180° - 44°
∠B = 136°
Similarly,
∠D = ∠B
∠D = 136°
Thus, the angles of a parallelogram are 44°,136°,44° and136° .
APPEARS IN
संबंधित प्रश्न
The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral.
Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.
In a parallelogram ABCD, ∠D = 135°, determine the measures of ∠A and ∠B
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 three sides of a quadrilateral are equal, it is a parallelogram .
If ABCD is a rhombus with ∠ABC = 56°, find the measure of ∠ACD.
Complete the following statement by means of one of those given in brackets against each:
Consecutive angles of a parallelogram are ...................
The figure formed by joining the mid-points of the adjacent sides of a quadrilateral is a
ABCD is a parallelogram and E and F are the centroids of triangles ABD and BCDrespectively, then EF =
Diagonals of a quadrilateral ABCD bisect each other. If ∠A= 45°, then ∠B =