The angles of a triangle measure (x+10)° , (x+20)° , and (x+30)° . Find the measure of the smallest angle.(1 point)
Responses
60°
60 degrees
50°
50 degrees
70°
70 degrees
40°
To find the smallest angle of a triangle with angles (x+10)°, (x+20)°, and (x+30)°, we need to find the smallest value of x among the three given expressions.
The smallest value of x would result in the smallest angle.
Given that (x+10)°, (x+20)°, and (x+30)° are angles of a triangle, their sum should be equal to 180°.
Therefore, we can set up the equation:
(x+10)° + (x+20)° + (x+30)° = 180°
Simplifying the equation, we get:
3x + 60 = 180
Subtracting 60 from both sides:
3x = 120
Dividing by 3 on both sides:
x = 40
So, when x = 40, the angles of the triangle become:
(x+10)° = 40 + 10 = 50°
(x+20)° = 40 + 20 = 60°
(x+30)° = 40 + 30 = 70°
Therefore, the measure of the smallest angle is 50°.