A side of the triangle below has been extended to form an exterior angle of 132°. Find the value of x.

Question

bottom 109°

Answer 1

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.

Answer 2

what's the answer bot its for a test please

Answer 3

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°.