Question

find the angle x in the above attached question
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Answer 1

Answer:

sum of exterior angles of Pentagon =360°

90+90+30+70+x= 360°

280°+x=360°

x= 80°

Answer 2

Answer:

x = 80°

Given:

A pentagon having 4 known angles and one unknown angle.

To Find:

Value of x.

Concept:

Sum of all interior angles of a pentagon is 540°

Solution:

Let the figure be ABCDE. Refer to attachment for details.

Let the $\angle$EAB , $\angle$ABC, $\angle$BCD and $\angle$CDE be a, b, c and d respectively.

The sum of linear pair (angles on a straight line) is 180°.

Therefore,

a + 30° = 180°

a = 180° - 30°

a = 150°

x + b = 180°

b = 180° - x ....(1)

c + 90° = 180°

c = 180° - 90°

c = 90°

d + 70° = 180°

d = 180° - 70°

d = 110°

We know that,

a + b + c + d + 90° = 540°

150° + (180° - x) + 90° + 110° + 90° = 540°

440° + 180° - x = 540°

620° - x = 540°

-x = 540° - 620°

-x = -80°

Cancelling (-) from both sides, we get:

x = 80°

Therefore, the answer is 80°

Other Formulas:

1) Sum of interior angles of a polygon where n is the number of sides of polygon= (2n - 4) * 90°

2)Number of sides of a regular polygon when exterior angle is given =$\dfrac{360^{\circ}}{x}$

where x is the exterior angle of a regular polygon

3) Sum of all exterior angles of any polgon = 360°

4) Number of diagonals of n sided polygon = $\dfrac{n(n-1)}{2}-n$

5) Sum of exterior and interior angle of a polygon of n sides = 180°