Question

In a pentagon, each of two angles has a measure of 68. Each of two others angles measures 142. What is the measure of the remaining angle?

Answer 1

120°

Step-by-step explanation

The sum of the measures of all the interior angles of a polygon with n sides is (n - 2)*180. So, for a pentagon, the sum of the measures of the interior angles is 540°.

In this pentagon, we know that there are two angles whose measures are 68°, another two angles whose measures are 142° and we have to find the measure of the last interior angle, x.

If we know that the sum of the interior angles is 540°, we can write an equation for x,

`68+68+142+142+x=540`

Combine like terms,

`420+x=540`

And subtract 420 from both sides,

`\begin{gathered} 420-420+x=540-420 \\ \\ x=120 \end{gathered}`

Hence, the measure of the remaining angle is 120°.