A side of the triangle below has been extended to form an exterior angle of 132°. Find the value of x.
bottom 109°
Let's call the bottom angle of the triangle "a" (109°).
Exterior angles of a triangle add up to 360°, so the exterior angle formed by extending the side is 360° - 109° = 251°.
Since this exterior angle is formed by extending a side of the triangle, it is also equal to the sum of the two remote interior angles. Let's call these angles "b" and "c".
b + c = 132° (given exterior angle)
b + c = 251° (since the exterior angle is also equal to the sum of b and c)
Now we have a system of equations:
a = 109°
b + c = 251°
Substituting the value of a into the second equation, we get:
109° + c = 251°
c = 251° - 109°
c = 142°
Since b + c = 132°, we can solve for b:
b + 142° = 132°
b = 132° - 142°
b = -10°
However, b must be positive, so this solution is not possible.
Therefore, there is no value of x that satisfies the given conditions.
what's the answer bot its for a test please
Apologies for my previous response. Let's re-evaluate the problem.
We are given that the bottom angle of the triangle is 109°. Let's call the exterior angle formed by extending the side "x".
The exterior angle is equal to the sum of the two remote interior angles. This can be written as:
x = angle b + angle c
We know that the sum of the angles in a triangle is 180°. Therefore, we can write:
angle b + angle c = 180° - 109° (since angle a is 109°)
angle b + angle c = 71°
Now, we can set up an equation using the information given in the problem:
x = angle b + angle c = 71°
So, the value of x is 71°.
To find the value of x, we need to use the property that the sum of the measures of the exterior angles of a triangle is always 360°.
In this case, we know that one of the exterior angles is 132°. Let's call the other two angles of the triangle A and B. Since the bottom angle is given as 109°, we can subtract this value from 360° to find the sum of angles A and B:
A + B = 360° - 109°
A + B = 251°
Now, we can set up an equation using the fact that the sum of the interior angles in a triangle is always 180°:
A + B + 109° = 180°
A + B = 71°
We now have a system of equations:
A + B = 251°
A + B = 71°
By subtracting the second equation from the first, we can eliminate A and B:
251° - 71° = 180°
So, we find that x is equal to 180°.