If the largest angle in a triangle is 70o, what is least possible value of the smallest angle of the triangle?
69o
1o
40o***
39o
41o
Is the correct answer 40?
Yes, the correct answer is 40°. The smallest angle of a triangle must be greater than 0° and less than the sum of the other two angles. Since the largest angle is 70°, the sum of the other two angles must be less than 110°. Therefore, the smallest angle could be as small as 40°.
Yes, the correct answer is 40°. To understand why, let's review some basics about triangles and their angles.
In any triangle, the sum of all the angles is always 180°. So, we can use this fact to find the value of the smallest angle in the triangle.
Given that the largest angle in the triangle is 70°, let's assign variables to the remaining two angles. Let's say the unknown smallest angle is 'x', and the second angle is 'y'.
Now, we have the following equation:
x + y + 70 = 180
To find the least possible value for the smallest angle, we need to consider the largest possible value for the other angle (y). The largest angle possible in a triangle is always less than 180°, so let's assume y is at its maximum value, which is 180 - 70 = 110°.
Substituting these values into the equation, we have:
x + 110 + 70 = 180
x + 180 = 180
x = 180 - 180
x = 0
However, a 0° angle is not possible in a triangle because it would essentially mean there is no line segment or side at that angle. Therefore, the smallest angle cannot be 0°.
Hence, the least possible value for the smallest angle is greater than 0°. Among the given options, the closest value to 0° is 40°. Therefore, the correct answer is 40°.
a+b+70 = 180
a+b = 110
max a = 70
so min b = 110-70 = 40 agree