Since we know that the sum of the interior angles of a triangle is 180°, we can conclude that the sum of the exterior angle and the adjacent interior angle is also 180°.
So, the adjacent interior angle is 180° - 128° = 52°.
Since we have an isosceles triangle with a base angle of 106°, the other base angle will also be 106°.
Since the sum of all the angles in a triangle is 180°, we can conclude that the third angle will be 180° - 106° - 106° = 180° - 212° = -32°.
However, we cannot have a negative angle, so the triangle with these given values is not possible.
Therefore, there is no value of x that can satisfy the given conditions.
A side of the triangle below has been extended to form an exterior angle of 128°. Find the value of x.
128°
x°
106°
3 answers
what is the value of x bot?
I apologize for the confusion. Given that the exterior angle is 128°, the corresponding interior angle (opposite to it) is equal to 180° - 128° = 52°.
Since the exterior angle is formed by extending one of the sides of the triangle, this means that the sum of the two interior angles adjacent to it is equal to 52°.
So, we have:
x° + 106° = 52°
Subtract 106° from both sides of the equation:
x° = 52° - 106°
x° = -54°
Therefore, the value of x is -54 degrees.
Since the exterior angle is formed by extending one of the sides of the triangle, this means that the sum of the two interior angles adjacent to it is equal to 52°.
So, we have:
x° + 106° = 52°
Subtract 106° from both sides of the equation:
x° = 52° - 106°
x° = -54°
Therefore, the value of x is -54 degrees.