Math / Geometry

QuestionWhat is the measure of each exterior angle of a regular hexagon? $40^{\circ}$ $45^{\circ}$ $60^{\circ}$ $72^{\circ}$

Studdy Solution

STEP 1

1. A regular hexagon has six equal sides and angles.
2. The sum of the exterior angles of any polygon is $360^\circ$ .

STEP 2

1. Determine the number of sides of the hexagon.
2. Calculate the measure of each exterior angle.

STEP 3

Identify the number of sides in a regular hexagon. A hexagon has:
$6 \quad \text{sides}$

STEP 4

Use the formula for the sum of the exterior angles of any polygon, which is always $360^\circ$ . Since a regular hexagon has equal exterior angles, each exterior angle is:
$\frac{360^\circ}{\text{number of sides}}$

STEP 5

Substitute the number of sides of the hexagon into the formula:
$\frac{360^\circ}{6}$

STEP 6

Calculate the division to find the measure of each exterior angle:
$\frac{360^\circ}{6} = 60^\circ$
The measure of each exterior angle of a regular hexagon is:
$\boxed{60^\circ}$

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QuestionWhat is the measure of each exterior angle of a regular hexagon? $40^{\circ}$ $45^{\circ}$ $60^{\circ}$ $72^{\circ}$

Studdy Solution

STEP 1

1. A regular hexagon has six equal sides and angles.
2. The sum of the exterior angles of any polygon is $360^\circ$ .

STEP 2

1. Determine the number of sides of the hexagon.
2. Calculate the measure of each exterior angle.

STEP 3

Identify the number of sides in a regular hexagon. A hexagon has:
$6 \quad \text{sides}$

STEP 4

Use the formula for the sum of the exterior angles of any polygon, which is always $360^\circ$ . Since a regular hexagon has equal exterior angles, each exterior angle is:
$\frac{360^\circ}{\text{number of sides}}$

STEP 5

Substitute the number of sides of the hexagon into the formula:
$\frac{360^\circ}{6}$

STEP 6

Calculate the division to find the measure of each exterior angle:
$\frac{360^\circ}{6} = 60^\circ$
The measure of each exterior angle of a regular hexagon is:
$\boxed{60^\circ}$

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QuestionWhat is the measure of each exterior angle of a regular hexagon? 40∘40^{\circ}40∘ 45∘45^{\circ}45∘ 60∘60^{\circ}60∘ 72∘72^{\circ}72∘

Studdy Solution

STEP 1

1. A regular hexagon has six equal sides and angles.2. The sum of the exterior angles of any polygon is 360∘ 360^\circ 360∘.

STEP 2

1. Determine the number of sides of the hexagon.2. Calculate the measure of each exterior angle.

STEP 3

Identify the number of sides in a regular hexagon. A hexagon has:6sides 6 \quad \text{sides} 6sides

STEP 4

Use the formula for the sum of the exterior angles of any polygon, which is always 360∘ 360^\circ 360∘. Since a regular hexagon has equal exterior angles, each exterior angle is:360∘number of sides \frac{360^\circ}{\text{number of sides}} number of sides360∘​

STEP 5

Substitute the number of sides of the hexagon into the formula:360∘6 \frac{360^\circ}{6} 6360∘​

STEP 6

Calculate the division to find the measure of each exterior angle:360∘6=60∘ \frac{360^\circ}{6} = 60^\circ 6360∘​=60∘ The measure of each exterior angle of a regular hexagon is:60∘ \boxed{60^\circ} 60∘​

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionWhat is the measure of each exterior angle of a regular hexagon? $40^{\circ}$ $45^{\circ}$ $60^{\circ}$ $72^{\circ}$

1. A regular hexagon has six equal sides and angles.
2. The sum of the exterior angles of any polygon is $360^\circ$ .

1. Determine the number of sides of the hexagon.
2. Calculate the measure of each exterior angle.

Identify the number of sides in a regular hexagon. A hexagon has:
$6 \quad \text{sides}$

Use the formula for the sum of the exterior angles of any polygon, which is always $360^\circ$ . Since a regular hexagon has equal exterior angles, each exterior angle is:
$\frac{360^\circ}{\text{number of sides}}$

Substitute the number of sides of the hexagon into the formula:
$\frac{360^\circ}{6}$

Calculate the division to find the measure of each exterior angle:
$\frac{360^\circ}{6} = 60^\circ$
The measure of each exterior angle of a regular hexagon is:
$\boxed{60^\circ}$