Question

The interior angles of a pentagon are 85, 106, (2x - 4), (3x - 15) and (200 - 2x). What is the
value of x? *​

Answer 1

Answer:

56°

Step-by-step explanation:

The sum of the interior angles of a pentagon is 540°.

=> 85° + 106° + 2x - 4 + 3x - 15 + 200 - 2x = 540°

=> 372 + 3x = 540°

=> 3x = 540° - 372°

=> 3x = 168°

=> x = 56°

Therefore, the value of x is 56°.

Answer 2

Answer:

56°

Step-by-step explanation:

Given,

Interior angles of a pentagon are :-

85° , 106° , (2x - 4)° , (3x - 15)° , (200 - 2x)°

To Find :-

Value of 'x'

How To Do :-

By adding all the interior angles of a Pentagon and equate it to Sum of total angles in a pentagon we can find the value of 'x'.

We Know That :-

Sum of Interior angles of a 'n' sided  Polygon = (n - 2) × 180°

As pentagon has '5' sides We will substitute 5 in place of 'n' :-

→ Sum of  interior angles in a Pentagon = (5 - 2) × 180°

= 3 × 180°

= 540°

Formula Required :-

Sum of interior angles in a Pentagon = 540°

Solution :-

Adding all interior angles and equating it to 540° :-

85° + 106° + (2x - 4)° + (3x - 15)° + (200 - 2x)° = 540°

85° + 106° + 2x° - 4° + 3x° - 15° + 200° - 2x° = 540°

Putting all Constant terms first and next variable terms after that :-

85° + 106° -  4° - 15° + 200° + 2x° + 3x° - 2x°  = 540°

372° + 3x° = 540°

3x° = 540° - 372°

3x° = 168°

x° = 168°/3

x° = 56°

∴ Value of 'x' = 56°.

Angles of a Pentagon :-

1) 85°

2) 106°

3) (2x - 4)° = 2(56°) - 4°

= 112° - 4°

= 108°

4) (3x - 15)° = 3(56°) - 15°

= 168° - 15°

= 153°

5) (200 - 2x)° = 200° - 2(56°)

= 200° - 112°

= 88°

∴ Interior Angles of a Pentagon are :- 85° , 106° , 108° , 153° , 88°.