Question

The opposite angles of a parallelogram are (3x+5)0 and (61-x)0 . Find the measure of four angles.

Answer 1

opposite angles of a parallelogram are equal and adjacent angles are supplementary.

(3x+5)° = (61-x)°
4 x = 56°
x = 14°

so the angles are :  3x+5 = 47°
            and   180° - 47° = 133°

Answer 2

The value of the four angles of the given parallelogram will be 47, 47, 133, and 133 degrees.

Given: The measure of the opposite angles of a parallelogram is given as 3x+5 degrees and 61-x degrees.

To Find: The true measure of the 4 angles.

Properties used - The opposite angles of a parallelogram are equal (1)

                              The adjacent interior angles of a parallelogram are supplementary. (2)

Solution:

3x+5 = 61-x {using property (1)}

4x = 56

x = 14

putting the value of x in the given 2 equations to get two angles out of the four angles of the parallelogram.

3*14+5 = 47 degrees

61-14 = 47 degrees

Now using property (2)  we will find the rest of the angles.

180 - 47 degrees = 133 degrees which will be the measure of the other two angles.

Hence the value of the four angles of the given parallelogram will be 47, 47, 133, and 133 degrees.