Question

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Find the measure of one interior angle and one exterior angle in each regular polygon. Round your answer to the nearest tenth if necessary 3aa and 4aa

Answer 1

3) Interior Angle = 90°

Exterior Angle = 90°

4) Interior Angle = 140°

Exterior Angle = 40°

Explanation:

A regular polygon is a polygon that has all sides of equal length and all angles of equal measure.

The interior angle of a regular polygon is the angle formed by two adjacent sides within the polygon.

The formula for the interior angle of a regular polygon is:

`\boxed{\begin{minipage}{6cm}\underline{Interior Angle of a Regular Polygon}\\\\Interior Angle $=((n-2)\cdot 180^(\circ))/(n)$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \end{minipage}}`

The exterior angle of a regular polygon is the angle formed by one side of the polygon and the extension of the adjacent side.

The sum of the exterior angles of any polygon is 360°.

Therefore, the formula for the exterior angle of a regular polygon is:

`\boxed{\begin{minipage}{6cm}\underline{Exterior Angle of a Regular Polygon}\\\\Exterior Angle $=(360^(\circ))/(n)$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \end{minipage}}`

Question 3

The given regular polygon has 4 sides.

Therefore substitute n = 4 into the formulas to find the measure of one interior angle and one exterior angle.

`\boxed{\begin{aligned}\textsf{Interior Angle}&=((4-2)\cdot 180^(\circ))/(4)\\\\&=(2\cdot 180^(\circ))/(4)\\\\&=(360^(\circ))/(4)\\\\&=90^(\circ)\end{aligned}}`

`\boxed{\begin{aligned}\textsf{Exterior Angle}&=(360^(\circ))/(4)\\\\&=90^(\circ)\end{aligned}}`

Question 4

The given regular polygon has 9 sides.

Therefore substitute n = 9 into the formulas to find the measure of one interior angle and one exterior angle.

`\boxed{\begin{aligned}\textsf{Interior Angle}&=((9-2)\cdot 180^(\circ))/(9)\\\\&=(7\cdot 180^(\circ))/(9)\\\\&=(1260^(\circ))/(9)\\\\&=140^(\circ)\end{aligned}}`

`\boxed{\begin{aligned}\textsf{Exterior Angle}&=(360^(\circ))/(9)\\\\&=40^(\circ)\end{aligned}}`

Answer 2

3.

one interior angle: 90°

one exterior angle: 90°

4.

one interior angle: 140°

one exterior angle: 40°

Explanation:

Note:
For interior angle:
The sum of the interior angles of a polygon is
`\boxed{\bold{(n-2)*180}}`, so the measure of one interior angle
`\boxed{\bold{((n-2)*180)/(n)}}` .where n is the number of sides. A regular polygon has all of its interior angles equal.

For exterior angle:

The sum of the exterior angles of a polygon is 360°, so the measure of one exterior angle is
`\boxed{\bold{(360)/(n)}}`.

The exterior angle of a polygon is supplementary to its interior angle, meaning that the two angles add up to 180 degrees.

Now for the question:

3.

no. of side (n)=4

one Interior angle: by substituting the value of n

we get,

`\boxed{\bold{((n-2)*180)/(n)=((4-2)*180)/(4)=90^o}}`

one exterior angle: by substituting the value of n

we get,

`\boxed{\bold{(360)/(4)=90^o}}`

4.

no. of side (n)=9

one Interior angle: by substituting the value of n

we get,

`\boxed{\bold{((n-2)*180)/(n)=((9-2)*180)/(9)=140^o}}`

one exterior angle: by substituting the value of n

we get,

`\boxed{\bold{(360)/(9)=40^o}}`