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Two parallel lines are cut by a transversal and form a pair of alternate exterior angles. One angle measures [tex]\((6x + 5)^\circ\)[/tex] and the other measures [tex]\((7x - 4)^\circ\)[/tex]. Explain how to determine what those angles actually measure.

1. Since the angles are alternate exterior angles and the lines are parallel, the angles are equal.
2. Set up the equation: [tex]\(6x + 5 = 7x - 4\)[/tex].
3. Solve for [tex]\(x\)[/tex].
4. Substitute the value of [tex]\(x\)[/tex] back into either angle expression to find the measure of the angles.

Sagot :

GinnyAnswer
To determine the measures of the alternate exterior angles formed by two parallel lines cut by a transversal, follow these steps:

1. Set up the Equation:
- Since the lines are parallel, the alternate exterior angles are equal.
- Therefore, we can write the equation:
[tex]\[ 6x + 5 = 7x - 4 \][/tex]

2. Solve for [tex]\(x\)[/tex]:
- First, simplify the equation by getting all terms involving [tex]\(x\)[/tex] on one side and constants on the other:
[tex]\[ 6x + 5 = 7x - 4 \][/tex]
Subtract [tex]\(6x\)[/tex] from both sides:
[tex]\[ 5 = x - 4 \][/tex]
Add 4 to both sides to isolate [tex]\(x\)[/tex]:
[tex]\[ 5 + 4 = x \][/tex]
Simplify:
[tex]\[ x = 9 \][/tex]

3. Substitute [tex]\(x\)[/tex] back into one of the angle expressions:
- Now that we have [tex]\(x = 9\)[/tex], we can substitute this value back into either of the angle expressions to find the actual measure of the angles.
- Using the first angle expression [tex]\((6x + 5)^\circ\)[/tex]:
[tex]\[ 6(9) + 5 = 54 + 5 = 59^\circ \][/tex]

4. Verify using the second angle expression:
- To ensure consistency, we can check the second angle expression [tex]\((7x - 4)^\circ\)[/tex]:
[tex]\[ 7(9) - 4 = 63 - 4 = 59^\circ \][/tex]
- Since both expressions yield the same angle measure, we have verified our solution.

Thus, the measure of each alternate exterior angle is [tex]\(59^\circ\)[/tex].
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