Math / Geometry

QuestionFind the sum of the measures of the angles of a four-sided polygon.

Studdy Solution

STEP 1

1. A four-sided polygon is also known as a quadrilateral.
2. The sum of the interior angles of a polygon can be calculated using a specific formula.

STEP 2

1. Recall the formula for the sum of interior angles of a polygon.
2. Apply the formula to a quadrilateral.

STEP 3

Recall that the sum of the interior angles of a polygon with $n$ sides is given by the formula:
$(n - 2) \times 180^\circ$

STEP 4

For a quadrilateral, the number of sides $n = 4$ . Substitute $n = 4$ into the formula:
$(4 - 2) \times 180^\circ$

STEP 5

Calculate the expression:
$2 \times 180^\circ = 360^\circ$
The sum of the measures of the angles of a four-sided polygon is:
$\boxed{360^\circ}$

Was this helpful?

QuestionFind the sum of the measures of the angles of a four-sided polygon.

Studdy Solution

STEP 1

1. A four-sided polygon is also known as a quadrilateral.
2. The sum of the interior angles of a polygon can be calculated using a specific formula.

STEP 2

1. Recall the formula for the sum of interior angles of a polygon.
2. Apply the formula to a quadrilateral.

STEP 3

Recall that the sum of the interior angles of a polygon with $n$ sides is given by the formula:
$(n - 2) \times 180^\circ$

STEP 4

For a quadrilateral, the number of sides $n = 4$ . Substitute $n = 4$ into the formula:
$(4 - 2) \times 180^\circ$

STEP 5

Calculate the expression:
$2 \times 180^\circ = 360^\circ$
The sum of the measures of the angles of a four-sided polygon is:
$\boxed{360^\circ}$

Get Studdy

Studdy solves anything!

Start learning now

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

QuestionFind the sum of the measures of the angles of a four-sided polygon.

Studdy Solution

STEP 1

1. A four-sided polygon is also known as a quadrilateral.2. The sum of the interior angles of a polygon can be calculated using a specific formula.

STEP 2

1. Recall the formula for the sum of interior angles of a polygon.2. Apply the formula to a quadrilateral.

STEP 3

Recall that the sum of the interior angles of a polygon with n n n sides is given by the formula:(n−2)×180∘ (n - 2) \times 180^\circ (n−2)×180∘

STEP 4

For a quadrilateral, the number of sides n=4 n = 4 n=4. Substitute n=4 n = 4 n=4 into the formula:(4−2)×180∘ (4 - 2) \times 180^\circ (4−2)×180∘

STEP 5

Calculate the expression:2×180∘=360∘ 2 \times 180^\circ = 360^\circ 2×180∘=360∘ The sum of the measures of the angles of a four-sided polygon is:360∘ \boxed{360^\circ} 360∘​

Get Studdy

Studdy solves anything!

Start learning now

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

1. A four-sided polygon is also known as a quadrilateral.
2. The sum of the interior angles of a polygon can be calculated using a specific formula.

1. Recall the formula for the sum of interior angles of a polygon.
2. Apply the formula to a quadrilateral.

Recall that the sum of the interior angles of a polygon with $n$ sides is given by the formula:
$(n - 2) \times 180^\circ$

For a quadrilateral, the number of sides $n = 4$ . Substitute $n = 4$ into the formula:
$(4 - 2) \times 180^\circ$

Calculate the expression:
$2 \times 180^\circ = 360^\circ$
The sum of the measures of the angles of a four-sided polygon is:
$\boxed{360^\circ}$