Answer to Question #252011 in Geometry for Safiah Mohamed

Question

Given: m<1+m<2=m<4

prove: m<3+m<1+m<2=180

Answer 1

Assuming this is about a 4-sided polygon whose angles will sum to 360, this is impossible to prove.

Let the angles be A, B, C and D.

If B+C+D=180(this is what we are trying to prove) then A, the remaining angle, is also 180 since 180+180=360.

However, if A is 180, then C+D is also 180,this is since the sum of all the angles in a polygon equals 360 and based on the given.

Substituting these values into A+B+(C+D) we get 180+B+180, which is a number greater than 360, and therefore not a quadrilateral.