A side of the triangle below has been extended to form an exterior angle of 64°. Find the value of
x
x.
Since the exterior angle equals the sum of the two opposite interior angles, we can subtract 64° from 180° to find that the opposite interior angle measures 116°.
Since x and the angle opposite it (116°) are both part of a straight line, they add up to 180°.
Therefore,
x + 116° = 180°
Subtracting 116° from both sides:
x = 64°
So the value of x is 64°.
To find the value of x, we need to use the fact that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.
In this case, the exterior angle is 64°, so the sum of the two opposite interior angles is also equal to 64°.
Let's call the two opposite interior angles a and b.
a + b = 64°
Since the exterior angle has been formed by extending one side of the triangle, one of the interior angles is 180° minus the exterior angle.
a = 180° - 64°
a = 116°
Now we can substitute the value of a into the equation to solve for b.
116° + b = 64°
b = 64° - 116°
b = -52°
However, angles cannot be negative, so this solution is not valid.
Therefore, there is no valid value of x that satisfies the given conditions.