Question

prove that in any triangle the outer angle at a vertex is equal to the sum of the inner angles at the other two vertices

Answer 1

Step-by-step explanation:

To prove: angleB + angleC = angleE

let the triangle be ABC.Then,produce side CA to D such that

angleA + angleE = 180 (by linear pair)

angleA = 180 - angleE_____1

we know that sum of all angles is a triangle is 180.then,

angleA + angleB + angleC=180

angleB + angleC = 180 - angleA ____2

put the value of angleA in 2, we get:

angleB + angleC = 180 - ( 180 - angleE)

angleB + angleC = 180 - 180 + angleE

angleB + angleC = angleE

Hence proved