Question

. The exterior angles of a triangle are (2x+10)⁰, (3x-5) ⁰ and (2x+40) ⁰.

i. Find the value of x.

ii. Find the smallest interior angle of the triangle.

iii. Find the largest interior angle of the triangle.

Answer 1

The exterior angles of a triangle are (2x+10)⁰, (3x-5) ⁰ and (2x+40) ⁰

To get interior angle for each , subtract from 180

`180-(2x+10)=170-2x\\180-(3x-5)=185-3x\\180-(2x+40)= 140-2x`

Sum of interior angles = 180

`170-2x+185-3x+140-2x=180`

`-7x+170+185+140=180\\-7x+495=180\\-7x+495-495=180-495\\-7x=-315\\x=45`

`170-2x=170-2(45)=80\\185-3x=185-3(45)=50\\140-2x=140-2(45)=50`

Answer: x=45

smaller angle =50 degree

largest interior angle = 80 degrees