Math / Geometry

QuestionThe diagram shows a regular polygon.
What is the value of $x$ ? Write your answer as an integer or as a decimal rounded to the nearest tenth. $x=\square^{\circ}$

Studdy Solution

STEP 1

1. The polygon in question is a regular polygon, specifically a square.
2. All interior angles of a square are equal.
3. The sum of the interior angles of a square is known.

STEP 2

1. Determine the sum of the interior angles of the square.
2. Calculate the measure of one interior angle of the square.

STEP 3

A square is a regular polygon with four sides. The formula for the sum of the interior angles of a polygon is given by:
$(n-2) \times 180^\circ$
where $n$ is the number of sides. For a square, $n = 4$ .

STEP 4

Substitute $n = 4$ into the formula:
$(4-2) \times 180^\circ = 2 \times 180^\circ = 360^\circ$
The sum of the interior angles of a square is $360^\circ$ .

STEP 5

Since a square is a regular polygon, all its interior angles are equal. Divide the sum of the interior angles by the number of sides to find the measure of one interior angle:
$\frac{360^\circ}{4} = 90^\circ$
The value of $x$ is:
$x = 90^\circ$

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QuestionThe diagram shows a regular polygon.
What is the value of $x$ ? Write your answer as an integer or as a decimal rounded to the nearest tenth. $x=\square^{\circ}$

Studdy Solution

STEP 1

1. The polygon in question is a regular polygon, specifically a square.
2. All interior angles of a square are equal.
3. The sum of the interior angles of a square is known.

STEP 2

1. Determine the sum of the interior angles of the square.
2. Calculate the measure of one interior angle of the square.

STEP 3

A square is a regular polygon with four sides. The formula for the sum of the interior angles of a polygon is given by:
$(n-2) \times 180^\circ$
where $n$ is the number of sides. For a square, $n = 4$ .

STEP 4

Substitute $n = 4$ into the formula:
$(4-2) \times 180^\circ = 2 \times 180^\circ = 360^\circ$
The sum of the interior angles of a square is $360^\circ$ .

STEP 5

Since a square is a regular polygon, all its interior angles are equal. Divide the sum of the interior angles by the number of sides to find the measure of one interior angle:
$\frac{360^\circ}{4} = 90^\circ$
The value of $x$ is:
$x = 90^\circ$

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QuestionThe diagram shows a regular polygon.What is the value of xxx ? Write your answer as an integer or as a decimal rounded to the nearest tenth. x=□∘x=\square^{\circ}x=□∘

Studdy Solution

STEP 1

1. The polygon in question is a regular polygon, specifically a square.2. All interior angles of a square are equal.3. The sum of the interior angles of a square is known.

STEP 2

1. Determine the sum of the interior angles of the square.2. Calculate the measure of one interior angle of the square.

STEP 3

A square is a regular polygon with four sides. The formula for the sum of the interior angles of a polygon is given by:(n−2)×180∘ (n-2) \times 180^\circ (n−2)×180∘where n n n is the number of sides. For a square, n=4 n = 4 n=4.

STEP 4

Substitute n=4 n = 4 n=4 into the formula:(4−2)×180∘=2×180∘=360∘ (4-2) \times 180^\circ = 2 \times 180^\circ = 360^\circ (4−2)×180∘=2×180∘=360∘The sum of the interior angles of a square is 360∘ 360^\circ 360∘.

STEP 5

Since a square is a regular polygon, all its interior angles are equal. Divide the sum of the interior angles by the number of sides to find the measure of one interior angle:360∘4=90∘ \frac{360^\circ}{4} = 90^\circ 4360∘​=90∘ The value of x x x is:x=90∘ x = 90^\circ x=90∘

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QuestionThe diagram shows a regular polygon.
What is the value of $x$ ? Write your answer as an integer or as a decimal rounded to the nearest tenth. $x=\square^{\circ}$

1. The polygon in question is a regular polygon, specifically a square.
2. All interior angles of a square are equal.
3. The sum of the interior angles of a square is known.

1. Determine the sum of the interior angles of the square.
2. Calculate the measure of one interior angle of the square.

A square is a regular polygon with four sides. The formula for the sum of the interior angles of a polygon is given by:
$(n-2) \times 180^\circ$
where $n$ is the number of sides. For a square, $n = 4$ .

Substitute $n = 4$ into the formula:
$(4-2) \times 180^\circ = 2 \times 180^\circ = 360^\circ$
The sum of the interior angles of a square is $360^\circ$ .

Since a square is a regular polygon, all its interior angles are equal. Divide the sum of the interior angles by the number of sides to find the measure of one interior angle:
$\frac{360^\circ}{4} = 90^\circ$
The value of $x$ is:
$x = 90^\circ$