Question

The interior angles of a pentagon are (y+13);(y+115);(y+23);(y+29);(y+40) find the value of each interior angle

Answer 1

Step-by-step explanation:

Given :-

The interior angles of a pentagon are (y+13)°,(y+115)°,(y+23)°,(y+29)°,(y+40)°

To find :-

Find the value of each interior angle ?

Solution :-

Given polygon = Pentagon

The number of sides in a Pentagon = 5

n = 5

Given that

The interior angles in Pentagon are (y+13)°,(y+115)°,(y+23)°,(y+29)°,(y+40)°

We know that

The sum of all interior angles in a regular polygon of n sides is (n-2)×180°

The sum of all interior angles in a regular Pentagon = (5-2)×180°

= 3×180° = 540°

=> (y+13)°+(y+115)°+(y+23)°+(y+29)°+(y+40)° = 540°

=> 5y + 220° = 540°

=> 5y = 540°-220°

=> 5y = 320°

=> y = 320°/5

=> y = 64°

Therefore, y = 64°

Now, The value of y+13 = 64°+13° = 77°

The value of y+115° = 64°+115° = 179°

The value of y+23° = 64°+23° = 87°

The value of y+29° = 64°+29° = 93°

The value of y+40° = 64°40° = 104°

Answer :-

The interior angles in a Pentagon are 77° , 179° , 87° , 93° and 104°

Used formulae:-

• The sum of all interior angles in a regular polygon of n sides is (n-2)×180°
• The sum of all interior angles in a Pentagon is 540°

Answer 2

EXPLANATION:-

We know that the sum of interior angles of pentagon is 540°

So the given interior angles of the pentagon must add up to 540

A.T.Q

y+13+y+115+y+23+y+29+y+40=540

5y+220=540

5y=540-220

5y=320

y=320/5

y=64

Hence the value of y is 64

Now let's calculate each angle:-

1)y+13

==>64+13

==>77

2)y+115

==>64+115

==>179

3)y+23

==>87

4)y+29

==>64+29

==>93

5)y+40

==>64+40

==>104

So the angles are 77°,179°,87°,93°,194°