The angles of a triangle measure (x+10)°, (x+20)°, and (x+30)°. Find the measure of the smallest angle.(1 point)

Question

Responses

70°
70 degrees

50°
50 degrees

40°
40 degrees

60°

Answer 1

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.