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The value of x (angle a) is 18 degrees, as determined using the exterior angle theorem.
The image shows a triangle with one side extended to form an exterior angle of 66 degrees. The question asks for the value of angle a.
To solve this problem, we can use the exterior angle theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle.
In this case, the exterior angle is 66 degrees, and the two remote interior angles are a and 48 degrees. Therefore, we can write the following equation:
66 = a + 48
Subtracting 48 from both sides of the equation, we get:
a = 66 - 48
a = 18
Therefore, the value of angle a is 18 degrees.
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