A side of the triangle below has been extended to form an exterior angle of 141°. Find the value of xx.
A triangle has interior angles that sum to 180°, so since a 141° exterior angle was formed by extending one side, the corresponding interior angle is 180° - 141° = <<180-141=39>>39°. Thus, the other two interior angles have a sum of 180° - 39° = 141°. Since a triangle only has 3 interior angles, these two angles must each be 141°/2 = <<141/2=70.5>>70.5°. Since angle x is adjacent to one of these 70.5° angles, we see that x = 180° - 70.5° = <<180-70.5=109.5>>109.5°. Thus, the value of x is x = <<109.5=109.5>>109.5°. Answer: \boxed{109.5}.
wrong.
Apologies for the mistake. Let's correct it.
An exterior angle of a triangle is equal to the sum of the two opposite interior angles. In this case, the exterior angle is 141°, and one of the opposite interior angles is x°. Therefore, the other opposite interior angle is 141° - x°.
Since the sum of the angles in a triangle is 180°, we have the equation:
x° + (141° - x°) + 39° = 180°
Combining like terms, we get:
180° - x° + 39° = 180°
Simplifying further:
219° - x° = 180°
Subtracting 219° from both sides:
-x° = -39°
Dividing both sides by -1:
x° = 39°
Therefore, the value of x is x = 39°.
To find the value of xx, we need to use the relationship between an exterior angle and its corresponding interior angles in a triangle.
First, let's label the points on the triangle. Suppose the extended side of the triangle meets the exterior angle at point A, and the adjacent sides of the triangle meet at points B and C, as shown below:
A
/ \
/ \
/ \
B-------C
Now, we know that an exterior angle of a triangle is equal to the sum of its two non-adjacent interior angles. In this case, the exterior angle is 141°, so we can write:
x + y = 141°
Next, we need to use the fact that the sum of the interior angles of a triangle is always 180°. In this case, the other two interior angles are x and z. So, we have:
x + y + z = 180°
Now, we have a system of equations:
x + y = 141°
x + y + z = 180°
To solve this system of equations, we can use substitution or elimination. Let's use the elimination method:
Subtracting the first equation from the second equation, we get:
(x + y + z) - (x + y) = 180° - 141°
This simplifies to:
z = 39°
Now, we can substitute this value back into the first equation:
x + y = 141°
x + 39° = 141°
Subtracting 39° from both sides, we get:
x = 141° - 39°
x = 102°
Therefore, the value of xx is 102°.