Question

the opposite angles of a parallelogram are (3x-2)°and (X+48)°.find the measure of each angle of the parallelogram​

Answer 1

Answer :

›»› The measure of each angle of the parallelogram are 96.6°, 81.2, 96.6° and 81.2°.

Step-by-step explanation :

Given :

• The opposite angles of a parallelogram = (3x - 2)° and (x + 48)°.

To Find :

• The measure of each angles of the parallelogram = ?

Knowledge required :

A parallelogram has four sides and four angles.

Opposite sides of a parallelogram are equal.

The sum of two adjacent angles of a parallelogram is 180°.

Solution :

We know that, if we are given with the two angles of a parallelogram then we have the required statement, that is,

→ The sum of two adjacent angles of a parallelogram = 180°.

By using the statement to calculate the angles of a parallelogram and substituting all four angles of a parallelogram in the given statement, we get :

→ (3x - 2) + (x + 48) = 180

→ 3x - 2 + x + 48 = 180

→ 3x + x - 2 + 48 = 180

→ 4x - 2 + 48 = 180

→ 4x + 46 = 180

→ 4x = 180 - 46

→ 4x = 134

→ x = 134/4

→ x = 33.2

Therefore,

The two angles of a parallelogram will be,

→ 1ˢᵗ angle = 3x - 2

→ 1ˢᵗ angle = 3 × 33.2 - 3

→ 1ˢᵗ angle = 99.6 - 3

→ 1ˢᵗ angle = 96.6.

→ 2ⁿᵈ angle = x + 48

→ 2ⁿᵈ angle = 33.2 + 48

→ 2ⁿᵈ angle = 81.2.

Now,

We know that, opposite sides of a parallelogram are equal. So,

→ 96.6° = 96.6°.

→ 81.2° = 81.2°

Hence, the measure of each angle of the parallelogram are 96.6°, 81.2, 96.6° and 81.2°.

Answer 2

Answer:

Given :-

• Opposite angle of Parallelogram are (3x -2) and (x + 48)

To Find :-

Angles

Solution :-

As we know that sum of two opposite sides of parallelogram is 180⁰

$\text {(3x - 2) + (x + 48) = 180}$

$\text{3x + x + 48 - 2 = 180}$

$\text{4x + 46 = 180}$

$\text{4x = 180 - 46}$

$\text{4x = 134}$

${ \rm{x = \dfrac{134}{4} }}$

$\purple\leadsto \frak \green{x = 33.2}$

Angles are

$\sf \: 3x - 2 = 3(33.2) - 2 = 96.6$

$\sf \: x + 48 = 33.2 + 48 = 81.2$

As we know that

$\sf \angle \: A = \angle \: C$

$\sf \angle \: B = \angle \: D$

Hence :-

Angle are 81.2⁰,96.6⁰,81.2⁰,96.6⁰