Proof that x = 11
Given: Angles 1 and 2 are a linear pair.
To prove: x = 11
Proof:
Linear angles are supplementary, meaning their sum is 180 degrees.
Therefore, the sum of angles 1 and 2 is 180 degrees.
We are given that the measure of angle 1 is 11x - 6 degrees.
We are given that the measure of angle 2 is 4x + 21 degrees.
Substituting these values into the equation above, we get:
11x - 6 + 4x + 21 = 180
Combining like terms, we get:
15x + 15 = 180
Subtracting 15 from both sides, we get:
15x = 165
Dividing both sides by 15, we get:
x = 11
Therefore, we have proven that x = 11.