Question

Four of the angles of a pentagon measure 85°, 110°, 135°, and 95°. Find the measure of the missing angle.

Answer 1

Sum of the angles of a n-sided polygon:

`\text{S}_{\text{n}}=180^\circ*(\text{n}-2)`

In this question, we have a pentagon, so

`\text{n}=5,`

then

`\text{S}_5=180^\circ*(5-2)`

`\text{S}_5=180^\circ*3`

`\text{S}_5=540^\circ \longleftarrow \ \text{sum of the measures of the internal\\}`

`\text{angles of a pentagon.}`

Let
`\text{x}` be the measure of the missing angle. So,

`85^\circ+110^\circ+135^\circ+95^\circ+\text{x}=\text{S}_5`

`425^\circ+\text{x}=540^\circ`

`\text{x}=540^\circ-425^\circ`

`\text{x}=115^\circ\longleftarrow \ \ \ \text{measure of the missing angle.}`

Tags: sum internal angle missing pentagon polygon plane geometry

Answer 2

A pentagon has five angles, and the sum of the angles of a pentagon is equal to 540°. Therefore, the measure of the fifth angle can be found by subtracting the sum of the given angles from 540°:

540° - (85° + 110° + 135° + 95°) = 540° - 425° = 115°.

Therefore, the measure of the missing angle is 115°.