The angles of a triangle add up to 180 degrees. The second angle is 12 degrees larger than the smallest angle. The third angle is 2 times as big as the smallest angle. Find the measure of the smallest angle (in degrees)

42°

Step-by-step explanation:

Sum of angle ABC = 180 degrees

if angle A = 1st angle

angle B = 2nd Angle

angle C = 3rd angle

(we are told angle b =, second angle is 12 degrees larger, 3rd angle 2 times bigger) so angle A is therefore the smallest angle

so our equation becomes

angle A + B + C = 180 degrees

angle (A + (12+A) + 2A) = 180 degrees

(we open brackets)

12 + A + A + 2A = 180 °

12 + 4A = 180°

4A = 180° - 12

4A = 168

A = 168/4

A = 42°

So the smallest angle A is 42°

(To see if it checks out

angle B = 12 + 42 = 54, angle C = 2*42 = 84, so

42° + 54° + 84° = 180°)

Let x = smallest angle

Let x + 12 = second angle

Let 2 (x + 12) = third angle

Here is the set up:

x + x + 12 + 2 (x + 12) = 180°

Take it from here.