Question

If the exterior angle of a triangle are (2x+10)°,(3x-5)° and (2x+40)° find the smallest interior angle ​

Answer 1

Sum of exterior angle of triangle=360°

2x+10+3x-5+2x+40=360°

(7x+45)°=360°

x=45°

Greatest exterior angle=(3x-5)°or (2x+40)°

=130°

Smallest interior angle=180°-130°

=50°

Answer 2

Answer:

$\huge\tt\underline \blue{Answer}$

_____________________________

$\tt\red{the~ sum ~of ~measure~ of ~exterior~ angles~ of ~triangle~ is ~360°.}$

$\tt{=>~(2x+10)~ +~(3x-5)~ +~(2x+40)~=~}\tt\red{360}$

$\tt{=>~2x~+~3x~+~2x~+~10~-~5~+~40~=~}\tt\red{360}$

$\tt{=>~7x~+~45~=~}\tt\red{360}$

$\tt{=>~}\tt\red{7x}\tt{~=~360~-~45}$

$\tt{=>~}\tt\red{x}\tt{~=~315/7}$

$\tt{=>~}\tt\red{x}\tt{~=~45}$

$\:$

$\tt{1st~ angle~ =~ 2x~+~10~=~2~×~45~+~10~=~90~+~10~=~}\tt\blue{100°}$

$\tt{2nd~ angle~ = ~3x~-~5~=~3~×~45~-~5~=~135~-~5~=~}\tt\blue{130°}$

$\tt{3rd ~angle ~= ~2x~+~40~=~2~×~45~+~40~=~90~+~40 ~=~}\tt\blue{130°}$

_____________________________

HOPE it HELPS

WITH REGARDS

❤ AR + NAV ❤