The problem asks us to find the sum of the interior angles of a polygon with 13 sides.

GeometryPolygonsInterior AnglesGeometric Formulas
2025/5/16

1. Problem Description

The problem asks us to find the sum of the interior angles of a polygon with 13 sides.

2. Solution Steps

To find the sum of the interior angles of a polygon with nn sides, we use the formula:
S=(n2)×180S = (n - 2) \times 180^{\circ}
In this problem, the polygon has 13 sides, so n=13n = 13.
Substituting n=13n = 13 into the formula, we get:
S=(132)×180S = (13 - 2) \times 180^{\circ}
S=(11)×180S = (11) \times 180^{\circ}
S=1980S = 1980^{\circ}

3. Final Answer

The sum of the interior angles of a polygon with 13 sides is 19801980^{\circ}.

Related problems in "Geometry"

The problem states that triangle $MNP$ is equilateral, and we are given the expressions for the side...

Equilateral TrianglePerimeterAlgebraic Equations
2025/5/16

The problem asks to find the distance between the point $(-2, 3)$ and the line $y = 2x + 1$.

Coordinate GeometryDistance FormulaLinesPoint-to-Line Distance
2025/5/16

Problem 32: A pool holds 450 cubic feet of water and has a height of 4.2 feet. We need to find the a...

AreaVolumePrismsTrianglesRectanglesSectorsPythagorean Theorem
2025/5/16

The problem asks to find the length of the midsegment $MN$ of a trapezoid $ABCD$. The lengths of the...

TrapezoidMidsegmentGeometric Formulas
2025/5/16

The problem states that the end of a charger plugged into a phone is an isosceles trapezoid. Given t...

GeometryTrapezoidIsosceles TrapezoidAnglesAngle Measurement
2025/5/16

We are given a rhombus $QRST$ and need to find the measures of angles 1, 3, and 4. We are given that...

RhombusAnglesGeometric PropertiesTrianglesAngle MeasurementDiagonals
2025/5/16

We are given a quadrilateral $ABCD$ with side lengths $AD = 4y - 20$, $AB = 8x - 34$, $BC = 6x - 4$,...

ParallelogramQuadrilateralAlgebraSolving Equations
2025/5/16

The problem states that $ABCD$ is a parallelogram. We are given that $m\angle DAB = 32^\circ$ and we...

ParallelogramAnglesGeometric Proof
2025/5/16

The problem asks to find the value of $y$ in a parallelogram, given that $m\angle D = (5y + 31)^\cir...

ParallelogramAnglesSolving EquationsGeometric Properties
2025/5/16

The problem asks to find the value of $x$ in a pentagon, where four of the angles are given as $68^\...

PolygonsInterior AnglesPentagon
2025/5/16