The angles of a triangle measure (x+10)°, (x+20)°, and (x+30)°. Find the measure of the smallest angle.(1 point)
Responses
70°
70 degrees
50°
50 degrees
40°
40 degrees
60°
To find the measure of the smallest angle, we need to find the smallest value for x+10.
Since the three angles of a triangle add up to 180 degrees, we can write the equation:
(x+10) + (x+20) + (x+30) = 180
Simplifying the equation, we get:
3x + 60 = 180
Subtracting 60 from both sides, we get:
3x = 120
Dividing both sides by 3, we get:
x = 40
Now, substituting x=40 into (x+10), we find the measure of the smallest angle:
(40+10) = 50°
Therefore, the measure of the smallest angle is 50 degrees.