Question

If the measure of angle 5 is (11 x minus 14) degrees and x = 6, which expression could represent the measure of angle 2?

3 lines intersect to form 6 angles. From top left, clockwise, the angles are 1, 2, 3, 4, 5, 6.
(8 x + 4) degrees
(9 x + 2) degrees
(20 x + 8) degrees
(18 x + 20) degrees

Answer 1

To find the measure of angle 5, we substitute \( x = 6 \) into the expression for angle 5:

\[
\text{Angle 5} = 11x - 14
\]
Substituting \( x = 6 \):
\[
\text{Angle 5} = 11(6) - 14 = 66 - 14 = 52 \text{ degrees}
\]

In a situation where three lines intersect, adjacent angles will be supplementary (i.e., they sum to 180 degrees). Therefore, angle 5 (52 degrees) has an adjacent angle that we will denote as angle 2.

Since angle 2 is adjacent to angle 5, we can express this relationship as:
\[
\text{Angle 2} + \text{Angle 5} = 180 \text{ degrees}
\]
Thus,
\[
\text{Angle 2} + 52 = 180
\]

Solving for angle 2, we find:
\[
\text{Angle 2} = 180 - 52 = 128 \text{ degrees}
\]

Now, we will check the provided expressions to see which one evaluates to 128 degrees when \( x = 6 \):

1. For the expression \( 8x + 4 \):
\[
8(6) + 4 = 48 + 4 = 52 \text{ degrees}
\]

2. For the expression \( 9x + 2 \):
\[
9(6) + 2 = 54 + 2 = 56 \text{ degrees}
\]

3. For the expression \( 20x + 8 \):
\[
20(6) + 8 = 120 + 8 = 128 \text{ degrees}
\]

4. For the expression \( 18x + 20 \):
\[
18(6) + 20 = 108 + 20 = 128 \text{ degrees}
\]

The two expressions that can represent the measure of angle 2 which equals 128 degrees are:

- \( 20x + 8 \)
- \( 18x + 20 \)

Thus, either \( 20x + 8 \) or \( 18x + 20 \) could represent the measure of angle 2.