Question

Find the measure of each interior angle

Decagon in which the measures of each interior angles are x + 5, x + 10, x + 20, x + 30, x + 35, x + 40, x + 60, x + 70, x + 80, and x + 90

Answer 1

The measure of each interior angle in a decagon is 144°.

Step-by-step explanation:

A decagon is a polygon with ten sides. To find the measure of each interior angle of a decagon, we can use the formula:

Sum of interior angles = (n - 2) * 180°

For a decagon, n = 10, so:

Sum of interior angles = (10 - 2) * 180° = 8 * 180° = 1440°

To find the measure of each interior angle, we divide the sum by the number of angles:

Measure of each interior angle = Sum of interior angles / Number of angles

Measure of each interior angle = 1440° / 10 = 144°

Therefore, each interior angle of the given decagon measures 144°.

Answer 2

`\bf \textit{sum of all interior angles of a polygon}\\\\ 180(n-2)\quad \begin{cases} n=\textit{number of sides}\\ ---------\\ n=10 \end{cases}\implies 180(10-2)\implies 1440\\\\ -------------------------------\\\\ \begin{array}{lclll} &x + 5\\&x + 10\\&x + 20\\&x + 30\\&x + 35\\&x + 40\\&x + 60\\&x + 70\\&x + 80\\+&x + 90\\ &----\\ &10x+440 \end{array}\implies \begin{array}{llll} 10x+440=1440 \\\\\\ 10x=1000 \\\\\\ x=\cfrac{1000}{10}\implies x=100 \end{array}`

so.. to get every angle, simply plug in 10 for "x" for each.