Two angles of an isosceles triangle are 68∘ and x∘. What is the sum of all the (distinct) possible values of x?
all the angles on a triangle egual 180 degrees so take 68 times 2 then subtract that by 180
there are two possible configurations
x+x+68 = 180: x=56
x+68+68 = 180: x=44
so, 56+44 = 100
To find the sum of all the distinct possible values of x, we first need to determine the value of x.
In an isosceles triangle, two angles are equal. So, the other two angles must also be 68°.
The sum of all three angles in any triangle is always 180°.
Let's set up an equation using the sum of angles in a triangle:
68° + 68° + x = 180°
Combine the like terms:
136° + x = 180°
To isolate x, subtract 136° from both sides of the equation:
x = 180° - 136°
Simplify:
x = 44°
Therefore, the value of x is 44°.
Now, to find the sum of all the distinct possible values of x, we need to consider if there are any other triangles with the same conditions.
If the isosceles triangle has two angles of 68° and x°, we can't have another triangle with the same conditions, as all sides and angles in an isosceles triangle are equal.
Therefore, the sum of all the distinct possible values of x is simply 44°.