6-1 First Day Interior Exterior Angle Sum

Last updated almost 2 years ago

16 questions

You can skip to about the 11:15 minute mark in this video to get to where I am at on these notes. 

A regular polygon is a polygon where all the sides are the same length and the angles are the same measurement. 

n  represents the number of sides in the polygon
Like a triangle has three sides. So for a triangle n = 3
A quadrilateral has four sides. So for a quadrilateral n = 4

Interior angle sum formula 

Single regular polygon interior angle formula

Exterior angle sum (exterior angles always add up to the same number, 360°)

Single regular polygon exterior angle formula

5.88

6-1 First Day Interior Exterior Angle Sum

6-1 First Day Interior Exterior Angle Sum

quadrilateral has 4 sides. So plugging into the formula.

(4-2) • 180

Find the value of x.

This is a quadrilateral. 4 sides.
So first
(4-2)•180
equals 360°.
So the 4 angles add up to 360.

x+(2x+5)+x+(2x+7) = 360

Then solve for x.

This is a quadrilateral. The 4 angles add up to 360.

Solve for x.

From the value of x that you had from the previous problem now find the measurement of angle K.

This is a pentagon.

(5-2)•180

540°

So in a pentagon the 5 angles add up to 540°

90°+(2x+10)°+x°+(2x-20)°+90°=540°

Solve for x.

This is a pentagon. The 5 angles add up to 540°

Find the value of x.

From the value of x that you had from the previous problem now find the measurement of angle Z.

These are exterior angles. Remember that the exterior angles always add up to 360°.

So

2x+88+x+10+x+2+52=360

Solve for x.

Solve for x.

Find the sum of the measures of the angles of a nonagon. (9 sides)

(n-2) • 180

(9-2) • 180

Find the sum of the measures of the angles of a heptagon. (7 sides)

(n-2) • 180

Find the measure of each interior angle of a regular quadrilateral.
n = 4

Here is the formula for this
So plugging in 4 for n.

Find the measure of each interior angle of a regular pentagon.
n = 5

Here is the formula for this

Find the measure of each angle of a regular octagon.
n = 8

So plugging in 8 for n

Find the measure of each angle of a regular nonagon.
n = 9

6-1 First Day Interior Exterior Angle Sum

6-1 First Day Interior Exterior Angle Sum

quadrilateral has 4 sides. So plugging into the formula. (4-2) • 180

Find the value of x. This is a quadrilateral. 4 sides. So first (4-2)•180equals 360°. So the 4 angles add up to 360. x+(2x+5)+x+(2x+7) = 360Then solve for x.

This is a quadrilateral. The 4 angles add up to 360. Solve for x.

From the value of x that you had from the previous problem now find the measurement of angle K.

This is a pentagon. (5-2)•180540°So in a pentagon the 5 angles add up to 540°90°+(2x+10)°+x°+(2x-20)°+90°=540°Solve for x.

This is a pentagon. The 5 angles add up to 540°Find the value of x.

From the value of x that you had from the previous problem now find the measurement of angle Z.

These are exterior angles. Remember that the exterior angles always add up to 360°.So 2x+88+x+10+x+2+52=360Solve for x.

Solve for x.

Find the sum of the measures of the angles of a nonagon. (9 sides)(n-2) • 180(9-2) • 180

Find the sum of the measures of the angles of a heptagon. (7 sides)(n-2) • 180

Find the measure of each interior angle of a regular quadrilateral. n = 4Here is the formula for thisSo plugging in 4 for n.

Find the measure of each interior angle of a regular pentagon. n = 5Here is the formula for this

Find the measure of each angle of a regular octagon. n = 8So plugging in 8 for n

Find the measure of each angle of a regular nonagon. n = 9

quadrilateral has 4 sides. So plugging into the formula.

(4-2) • 180

Find the value of x.

This is a quadrilateral. 4 sides.
So first
(4-2)•180
equals 360°.
So the 4 angles add up to 360.

x+(2x+5)+x+(2x+7) = 360

Then solve for x.

This is a quadrilateral. The 4 angles add up to 360.

Solve for x.

This is a pentagon.

(5-2)•180

540°

So in a pentagon the 5 angles add up to 540°

90°+(2x+10)°+x°+(2x-20)°+90°=540°

Solve for x.

This is a pentagon. The 5 angles add up to 540°

Find the value of x.

These are exterior angles. Remember that the exterior angles always add up to 360°.

So

2x+88+x+10+x+2+52=360

Solve for x.

Find the sum of the measures of the angles of a nonagon. (9 sides)

(n-2) • 180

(9-2) • 180

Find the sum of the measures of the angles of a heptagon. (7 sides)

(n-2) • 180

Find the measure of each interior angle of a regular quadrilateral.
n = 4

Here is the formula for this
So plugging in 4 for n.

Find the measure of each interior angle of a regular pentagon.
n = 5

Here is the formula for this

Find the measure of each angle of a regular octagon.
n = 8

So plugging in 8 for n

Find the measure of each angle of a regular nonagon.
n = 9