meredith48034
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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

NO LINKS URGENT HELP PLEASE Find the measure of one interior angle and one exterior angle in each regular polygon Round your answer to the nearest tenth if nece class=


Answer :

msm555

Answer:

3.

one interior angle: 90°

one exterior angle: 90°

4.

one interior angle: 140°

one exterior angle: 40°

Step-by-step explanation:

Note:
For interior angle:
The sum of the interior angles of a polygon is  [tex]\boxed{\bold{(n-2)*180}}[/tex],  so the measure of one interior angle[tex]\boxed{\bold{\frac{(n-2)*180}{n}}}[/tex] .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  [tex]\boxed{\bold{\frac{360}{n}}}[/tex].

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,

[tex]\boxed{\bold{\frac{(n-2)*180}{n}=\frac{(4-2)*180}{4}=90^o}}[/tex]

one exterior angle: by substituting the value of n

we get,

[tex]\boxed{\bold{\frac{360}{4}=90^o}}[/tex]

4.

no. of side (n)=9

one Interior angle: by substituting the value of n

we get,

[tex]\boxed{\bold{\frac{(n-2)*180}{n}=\frac{(9-2)*180}{9}=140^o}}[/tex]

one exterior angle: by substituting the value of n

we get,

[tex]\boxed{\bold{\frac{360}{9}=40^o}}[/tex]

semsee45

Answer:

3)  Interior Angle = 90°

    Exterior Angle = 90°

4)  Interior Angle = 140°

    Exterior Angle = 40°

Step-by-step 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:

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

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:

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

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.

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

[tex]\boxed{\begin{aligned}\textsf{Exterior Angle}&=\dfrac{360^{\circ}}{4}\\\\&=90^{\circ}\end{aligned}}[/tex]

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.

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

[tex]\boxed{\begin{aligned}\textsf{Exterior Angle}&=\dfrac{360^{\circ}}{9}\\\\&=40^{\circ}\end{aligned}}[/tex]