Question

Two opposite angles of a parallelogram are (3x - 2)^0.
and (50 - x)^0
. Find the

measure of each angle of the parallelogram.​

Answer 1

Correct Question :

Two opposite angles of a parallelogram are (3x - 2)°, and (50 - x)°. Find the measure of each angle of the parallelogram.

Answer :

The measure of all the angles of parallelogram is

• 37°
• 143°
• 37°
• 143°

Step-by-step explanation :

To Find,

• The measure of all the angles of a parallelogram

Solution,

Let us assume ( 3x - 2 ) and ( 50 - x ) be first angle and second angle respectively,

Given that,

The opposite angles of the parallelogram are

• ( 3x - 2 )°
• ( 50 - x )°

As we know that,

Opposite angles of a parallelogram are equal. Therefore,

➠ ( 3x - 2 ) = ( 50 - x )

➠ 3x - 2 = 50 - x

➠ 3x + x = 50 + 2

➠ 4x = 52

➠ x = 52 / 4

➠ x = 13

Hence, the value of x is 13.

∴ The measure of the opposite angles are,

• ( 3x - 2 )

➠ 3 × 13 - 2

➠ 39 - 2

➠ 37°

Hence, the measure of both the opposite angles of parallelogram ( 1st angle & 3nd angle ) is 37°. As, opposite angles of a parallelogram are equal.

Now, the measure of the other sides of the parallelogram are,

➠ 180° - 37° ..... adjacent angles

➠ 143°

Hence, The measure of ( 2nd angle and 4th angle ) is 143°, As opposite angles of a parallelogram are equal.

∴ The measure of all the angles of parallelogram are 37°, 143°, 37° and 143°.