Question

four angles of quadrilateral are (3x+20)°, (x-30)°, (2x+10)° and 2x° . value of X is​

Answer 1

We have:-

The angles of a quadrilateral:

• (3x + 20)°
• (x - 30)°
• (2x + 10)°
• 2x°

To calculate:-

• The value of x here?

Solution:-

All the angles of a quadrilateral add upto 360° because it can be divided into 2 triangles and each triangle have a total sum of angles 180°.

Then,

➛ 3x + 20° + x - 30° + 2x + 10° + 2x = 360°

➛ 3x + x + 2x + 2x + 20° - 30° + 10° = 360°

➛ 8x = 360°

➛ x = 360° / 8

➛ x = 45°

Then the angles are:

• 3(45°) + 20° = 155°
• 45° - 30° = 15°
• 2(45°) + 10° = 100°
• 2(45°) = 90°

Quick check:-

Let's see whether the angles add upto 360° or not.

= 155° + 15° + 100° + 90°

= 360° ✓

Hence, Verified!!

Answer 2

Answer:

$\huge \bf \: solution$

It is given that it's a quardilateral. So, therefore it's angle sum will be 360⁰.

Then,

$\sf \: (3x + 20) + (x - 30) + (2x + 10) + (2x) = 360$

Step 1

Remove the brackets

$\sf \: 3x + 20 + x - 30 + 2x + 10 + 2x = 360$

Step 2

Take variable and constant in different group

$\sf \: 3x + x + 2x + 2x + 20 - 30 + 10$

Step 3

Adding variable and constant

$\sf \: 8x + 0 = 360$

Step 4

Removing 0

$\sf8x = 360$

Step 5

Dividing 8 from 360

$\sf \: x = \frac{360}{8} = 45$

Now,

Angles

$\sf \: 3x + 20 = 3 \times 45 + 20 = 155$

$\sf \: x - 30 = 45 - 30 = 15$

$\sf \: 2x + 10 = 2(45) + 10 = 100$

$\sf \: 2x = 2(45) = 90$

Let's verify

$\rm \: 155 + 15 + 100 + 90 = 360$

$\rm \: 170 + 190 = 360$

$\rm \: 360 = 360$

LHS = RHS