Question

The exterior angles of a triangle are 3y0, 4y0 and 5y0.

i. Find the value of y.
ii. Find the smallest interior angle of the triangle.

Answer 1

i) y = 30°

ii) 30°

Explanation:

Total exterior angle = 360

3y° + 4y° + 5y° = 360

12y° = 360

y° = 30°

Interior angle = 180 - exterior angle

Interior angle will be the smallest when the exterior angle is the greatest, which is:

5y = 5(30) = 150°

Smallest interior angle = 180 - 150

= 30°

Answer 2

i. 30 degrees

ii. 30 degrees

Explanation:

The exterior angles of a triangle always add up to 360 degrees. Using this, you can set up the following equation.

3y+4y+5y=360

y=30 degrees

The smallest interior angle corresponds to the largest exterior angle. 5y=5*30= 150. Subtracting this from 180 you get 30 degrees, or the smallest interior angle. Hope this helps!