Question

Find the sum of the interior angles, then solve for x.E 135° F 147° D 110° G -128° Н 118° J 135° Sum of Interior Angles: type your answer... X= type your answer...

Answer 1

The shape that is shown in the image is a heptagon (it has 7 sides), to determine the sum of the interior angles of any shape you have to subtract 2 to the number of sides of the shape and multiply the result by 180. The formula is as follows:

`(n-2)\cdot180`

Where n represents the number of sides.

The sides on the heptagon are n=7, replace this value in the formula and you get the sum of the inner angles of the shape:

`(7-2)\cdot180=5\cdot180=900º`

The sum of the interior angles of the heptagon is 900º

Now that you know how much do the interior angles add up to we can calculate the value of x as follows:

`\angle D+\angle E+\angle F+\angle G+\angle H+\angle J+\angle K=900º`

Replace the expression with the known measures of all angles and calculate for the missing one

`\begin{gathered} 110+135+147+128+118+135+x=900 \\ 773+x=900 \\ 773-773+x=900-773 \\ x=127º \end{gathered}`

The value of x is 127º