Question

One pair of opposite angles in a parallelogram measures (3x - 2)° and (50 - x)°. Find all
the angles of the parallelogram.
​

Answer 1

Answer:

• Angles of parallelogram are 37°, 143°, 37° and 143°.

Step-by-step explanation:

Given :-

• One pair of opposite angles of parallelogram are (3x - 2)° and (50 - x)°.

To find :-

• All angles of parallelogram.

Solution :-

We know,

Opposite angles of parallelogram are equal.

So,

⇒3x - 2° = 50° - x

⇒3x + x = 50° - 2°

⇒4x = 52°

⇒x = 52°/4

⇒x = 13°

Opposite angles :

• 3x - 2° = 3×13° - 2° = 37°

• 50° - x = 50° - 13° = 37°

Sum of adjacent angles of parallelogram is 180°.

So,

⇒∠1 + 50° - x = 180°

⇒∠1 + 37° = 180°

⇒∠1 = 180° - 37°

⇒∠1 = 143°

Now,

Angle opposite to ∠1 is also 143°. Because opposite angles of parallelogram are equal.

Therefore,

Angles of parallelogram are 37°, 143°, 37° and 143°.

Answer 2

Answer:

Given :-

• Measure of two opposite sides of Parallelogram measure (3x -2)⁰ and (50 - x)⁰

To Find :-

Angles

SoluTion :-

As we know that

Opposite sides of Parallelogram are equal.

$\tt \: 3x - 2 = 50 - x$

$\tt \: 3x + x = 50 + 2$

$\tt \: 4x = 50 + 2$

$\tt \: 4x = 52$

$\tt \: x = \dfrac{52}{4}$

$\tt \: x = 14$

Opposite angles are

$\tt \: 3x - 2 = 3 \times 13 - 2 = 39 - 2 = 37$

$\tt \: 50 - x = 50 - 13 = 37$

Now,

Adjacent sides measure 180⁰

$\tt \angle \: 1 + 50 - x = 180$

$\tt \angle \: 1 + 37 = 180$

$\tt \angle \: 1 = 180 - 37$

$\tt \angle \: 1 = 143$

Angles are :-

143⁰,37⁰,143⁰,37⁰