Question

I haven't been able to figure out the answer/formula for this problem. Does anyone know how to do this?

Answer 1

Answer is x=61°

Explanation:

If we have to calculate the sum of internal angles of any figure whether it is triangle,rectangle,pentagon or any figure we join one point of any side to all points of the figure.

We find the triangles inside the figure like in triangle there will be only one triangle,in rectangle two triangles,in pentagon there are three triangle inside the figure.

So we can say in a triangle⇒Number of triangles=1

Then total of all angles=180°

In a rectangle ⇒ Number of triangles = 2

Then sum of all angles = 180°×2=360°

In a pentagon number of triangles =3

So total of all internal angles = 180°×3=540° and so on

Now we can say in a polygon total of all internal angles = (n-2)×180°

Now we come to the figure given

(n-2)×180°=sum of all internal angles

(5-2)×180°=x+90+107+144+138

540 = x+479

x= 540-479

x=61°

Answer 2

x = 61°

Explanation:

Sum of interior angles of an n sided polygon is
`(n-2)*180`

where n is the number of sides

The figure is a pentagon (5 sided figure), so plug in 5 into n in the formula to get the sum of all the angles:

`(n-2)*180\\=(5-2)*180\\=3*180\\=540`

Now summing all the angles in and equation and equating to 540, we can solve for x (remember one is a 90 degree angle):

`x+138+144+107+90=540\\x+479=540\\x=540-479\\x=61`

Hence x = 61°