A side of the triangle below has been extended to form an exterior angle of 135°. Find the value of x.
122° and x°.
Since the exterior angle of a triangle is equal to the sum of the two interior opposite angles, we can set up the following equation:
x + 122° = 135°
Subtract 122° from both sides to isolate x:
x = 135° - 122°
Simplify the equation:
x = 13°
Therefore, the value of x is 13°.
To find the value of x, we can use the fact that the sum of the exterior angles of a triangle is always 360°.
In this case, the exterior angle is given as 135°.
Let's denote the interior angles of the triangle as A, B, and C, and let x be the measure of angle A.
We know that the exterior angle is equal to the sum of the two non-adjacent interior angles.
So, we have:
x + 122° = 135°
Subtracting 122° from both sides, we get:
x = 135° - 122°
Simplifying, we find:
x = 13°
To find the value of x, we can use the fact that the sum of the measures of the exterior angles of a triangle is always 360 degrees.
In this case, we are given that one of the exterior angles is 135 degrees. Let's call the other two angles of the triangle A and B.
Since the sum of the exterior angles is 360 degrees, we can write the equation:
A + B + 135 = 360
To find the value of A, we need to subtract B from both sides of the equation:
A = 360 - B - 135
A = 225 - B
Now, let's consider the interior angles of the triangle. We know that the sum of the measures of the interior angles of a triangle is always 180 degrees.
We can write another equation using this property:
A + B + x = 180
To solve for x, we need to substitute the value of A that we found earlier:
(225 - B) + B + x = 180
Simplifying the equation:
225 + x = 180
Now, let's solve for x by subtracting 225 from both sides of the equation:
x = 180 - 225
x = -45
Therefore, the value of x is -45 degrees.
Note: It's unusual to have a negative angle measure in this context, so it's possible that there may be an error in the question or the calculations. Double-checking the information provided is always a good idea.
That is wrong bot
Apologies for the incorrect response. Let's solve the problem correctly:
The sum of the exterior angles of any polygon is always 360 degrees. In this case, we have the exterior angle given as 135°.
Let's denote the interior angles of the triangle as A, B, and C. We know that the exterior angle is equal to the sum of the two non-adjacent interior angles.
So, we have:
A + 122° = 135°
Subtracting 122° from both sides, we get:
A = 135° - 122°
Simplifying, we find:
A = 13°
Therefore, the value of A (or x) is 13°.