Question

two opposite angles of parallelogram are (3x-2)° and (50-x)°. Find the angles of parallelogram.

Answer 1

As we know, opposite angles of a parallelogram are equal.
hence, 3x-2 = 50-x
3x+x = 50+2
4x = 52
x = 52/4
x = 13

(3x-2)= 13×3-2 = 39-2 = 37 degrees
(50-x)= 50-13 = 37 degrees
and the rest two angles will also be equal
(143 degrees both)

Answer 2

Given:

The two opposite angles of a parallelogram are (3x-2)° and (50-x)°.

To find:

The angles of a parallelogram.

Solution:

As we know that in a parallelogram, the two opposite angles are equal. So, according to the question, the two opposite angles of a parallelogram are (3x-2)° and (50-x)°.

Hence, from the opposite angle property of a parallelogram, we have,

$3x - 2 = 50 - x$

On solving above,

$4x = 52$

$x = 13$

So, using value of x, the one angle of a parallelogram =

$(50 - x)°$

$= (50 - 13)°$

$= 37°$

Also, the adjacent angles of a parallelogram is equal to 180°. So, let the adjacent angle of 37° be m°.

So, we have

$m + 37= 180$

$m = 143°$

Thus, the two angles of a parallelogram is 37° while the rest two angles have a measure of 143°. This is because, the opposite angles of a parallelogram are equal.

Hence, the four angles of a parallelogram are 37°, 143°, 37° and 143°.