Question

two opposite angles of a parallogram are (4X+3)and(57+2x) find all the angles of parallogram​

Answer 1

Step-by-step explanation:

4X+3 = 57+2x

2X = 54

X = 27

first angle = 4×27 + 3 = 111°

third angle = 111°

second angle = 180-111 = 69°

fourth angle = 69°

Answer 2

• Angles of parallelogram are 111°, 69°, 111° and 69° respectively.

Step-by-step explanation:

Given:-

• Two opposite angles of parallelogram are (4x + 3) and (57 + 2x).

To find:-

• All angles of parallelogram.

Solution:-

We know that,

Opposite angles of parallelogram are equal.

So,

➝ 4x + 3 = 57 + 2x

• 4x + 3 and 57 + 2x are opposite angles.

➝ 4x - 2x = 57 - 3

➝ 2x = 54

➝ x = 54/2

➝ x = 27

Angles :

4x + 3 = 4×27 + 3 = 111°

57 + 2x = 57 + 2×27 = 111°

Let, the angle adjacent to 4x + 3 be ∠1.

And, Angle opposite of ∠1 be ∠2.

We know also know that,

Sum of two adjacent angles of parallelogram is equal to 180°.

So,

➝∠1 + 4x + 3 = 180°

➝∠1 + 111° = 180°

➝∠1 = 180° - 111°

➝∠1 = 69°

• Opposite angles of parallelogram are equal.

So, ∠1 = ∠2 = 69°

Therefore,

Angles of parallelogram are 111°, 69°, 111° and 69° respectively.