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A side of the triangle below has been extended to form an exterior angle of 136°. Find the value of x?

User Andrew Lee
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Answer:

To find the value of x in the given triangle, we need to apply the properties of exterior angles of triangles.

In a triangle, the sum of the measures of the three exterior angles is always 360 degrees. Therefore, we can determine the value of x by subtracting the given exterior angle from 360 degrees.

Let's denote the three angles of the triangle as A, B, and C. The exterior angle formed by extending side BC is denoted as angle D.

According to the property of exterior angles, angle D is equal to the sum of angles A and B. Therefore, we have:

D = A + B

Since angle D is given as 136 degrees, we can write:

136 = A + B

Now, let's consider the sum of all three angles in a triangle:

A + B + C = 180

We can rearrange this equation to solve for C:

C = 180 - (A + B)

Substituting the value of A + B from the previous equation, we get:

C = 180 - 136

C = 44

So, we have found that angle C is equal to 44 degrees.

Now, to find the value of x, we need to consider the relationship between angle C and angle x. In a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can write:

x + C + A = 180

Substituting the values we know:

x + 44 + A = 180

Since we don't have any information about angle A, we cannot determine its exact value. However, we can express it in terms of x:

A = 180 - (x + 44)

A = 136 - x

Therefore, the value of x cannot be determined without additional information about angle A.

Explanation:

User Pettinato
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