Sum of inner angles

Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees.

Correct answer:

Did you find an error or inaccuracy? Feel free to write us. Thank you!

You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions:

Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
Triangle
Prove whether you can construct a triangle ABC, if a=9 cm, b=6 cm, c=10 cm.
n-gon
Gabo draws n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon?
Prove
Prove that k1 and k2 are the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x²+y²+2x+4y+1=0 k2: x²+y²-8x+6y+9=0
Angles in a triangle
The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°. What sizes have other angles in a triangle?
Three numbers
How much we increases the sum of three numbers when the first enlarge by 14, second by 15 and third by 16? Choose any three two-digit numbers and prove results.
Octahedron - sum
On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also
N-gon angles
What is the sum of interior angles 8-gon? What is the internal angle of a regular convex 8-polygon?
Workers
Three factory operators produced 480 units in 50 minutes. How many hours worked? I'm trying to prove or disapprove the idea that the company tell me that it's 2.5 hours. So what is right? Thank you, Petra
Proof PT
Can you easily prove Pythagoras theorem using Euclidean theorems? If so, do it.
Angles of a hexagon
Find the interior angles of a hexagon if the sizes of the angles form an arithmetic sequence, and the smallest angle is 70°.
N-gon
How many diagonals have convex 11-gon?
Diagonal in rectangle
In that rectangle ABCD is the center of BC point E and point F is center of CD. Prove that the lines AE and AF divide diagonal BD into three equal parts.
See harmonics
It is true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. Central segment crosses the intersection of the diagonals and is parallel to the bases.
Diagonals in diamond
In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
Dodecagon
Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
Truncated cone
Calculate the height of the rotating truncated cone with volume V = 1354 cm³ and a base radii r₁ = 9.1 cm and r₂ = 5.4 cm.