Question
Find the smallest angle of the triangle with measures 50°, 3x°, and (x+10)°
Answers
GPT 3.5
To find the smallest angle of the triangle, we need to determine the value of x. We know that the sum of the angles in a triangle is 180°. Therefore, we can set up the equation:
50° + 3x° + (x+10)° = 180°
Combining like terms, we have:
50° + 4x° + 10° = 180°
Combining constants, we have:
60° + 4x° = 180°
Next, we isolate 4x° by subtracting 60° from both sides:
4x° = 180° - 60°
4x° = 120°
Finally, we divide both sides of the equation by 4 to solve for x:
x° = 120°/4
x° = 30°
Now that we have found the value of x, we can substitute it back into our triangle to find the smallest angle. The angles are 50°, 3x° which is 3(30°) = 90°, and (x+10)° which is 30° + 10° = 40°.
Therefore, the smallest angle of the triangle is 40°.
50° + 3x° + (x+10)° = 180°
Combining like terms, we have:
50° + 4x° + 10° = 180°
Combining constants, we have:
60° + 4x° = 180°
Next, we isolate 4x° by subtracting 60° from both sides:
4x° = 180° - 60°
4x° = 120°
Finally, we divide both sides of the equation by 4 to solve for x:
x° = 120°/4
x° = 30°
Now that we have found the value of x, we can substitute it back into our triangle to find the smallest angle. The angles are 50°, 3x° which is 3(30°) = 90°, and (x+10)° which is 30° + 10° = 40°.
Therefore, the smallest angle of the triangle is 40°.