Question

Two adjacent angles of a parallelogram are (3x-4)° and (3x+10)°.Find the angles of parallelogram.

Answer 1

we know that sum of adjacent angle in a parallelogram is 180.
3x-4+3x+10=180
6x+6=180
6x=180-6
x=174/6
x=29
therefor 1st angle=3*29-4=83
2nd angle=3*29+10=97

Answer 2

Given,

Two adjacent angles of a parallelogram are (3x-4)° and (3x+10)°

To find,

The angles of the parallelogram.

Solution,

We can simply solve this mathematical problem using the following process:

As per mensuration;

Any two adjacent angles of a parallelogram are supplementary. {Statement-1}

And, opposite angles of a parallelogram are equal.

{Statement-2}

Now, according to the question;

(3x-4)° + (3x+10)° = 180°

(3x-4)° + (3x+10)° = 180°{according to statement-1}

=> 6x + 6 = 180

=> x + 1 = 30

=> x = 29

Now, the two adjacent angles of the given parallelogram are:

the two adjacent angles of the given parallelogram are:(3x-4)° and (3x+10)°

=> (3×29 - 4)° and (3×29 + 10)°

=> 83° and 97°

Now, according to statement-2, as opposite angles are equal, so out of the 4 angles of the parallelogram, 1 pair of opposite angles measure 97° and the other pair of opposite angles measure 83°, respectively.

Hence, the four angles of the parallelogram are 97°, 83°, 97°, and 83°, respectively.