Question

how many Triangles are there in a heptagon if drawn from a single vertex? Find the sum of the all interior angles of the heptagon based on the Triangles so formed

Answer 1

15 Triangles are there in a heptagon if drawn from a single vertex

5 Non - intersecting Triangle  are there in a heptagon if drawn from a single vertex

Step-by-step explanation:

A heptagon has 7 Sides & 7 Vertex

To form a Triangle we need Three Vertex

Number of Triangles = ⁷C₃ = 35

Number of Triangles in a Heptagon if drawn from a single vertex

Hence 1 Vertex is Fixed

now we have to choose two vertex for 6 Vertex

number of possible triangles = ⁶C₂  = 15

Number of Triangles in a Heptagon if drawn from a single side

then 2 Vertex are fixed

hence remaining 1 vertex can be selected from 5 vertex in 5 ways

if Non - intersecting Triangle

Then let say Vertex are 1 , 2 , 3  , 4 , 5 , 6 , 7

and Triangles from Vertex 1

123  , 134 , 145 , 156 , 167

5  Triangles - Sum of Angle sof 5 Triangles = 5 * 180° = 900°

sum of the all interior angles of the heptagon = 900°

Learn more:

Verify that the sum of measure of exterior angles of any polygon is ...

https://brainly.in/question/10556355

Answer 2

Answer:

sorry but ans Is 900

Step-by-step explanation:

sum of Interior angle is 180'

sides of heptagon is 5 sides

so 5 × 180 = 900 Ans

so easy method