Question

question 4 (5 points)
when two parallel lines are cut by a transversal, the alternate exterior angles are
a) complementary.
b) supplementary.
c) not congruent.
d) congruent.
question 5 (5 points)
what is the slope of a line perpendicular to y = -5x + 6?
a) 5
b) -1/5
c) -5
d) 1/5

Explanation:

Question 4

Step1: Recall Alternate Exterior Angles Theorem

When two parallel lines are cut by a transversal, alternate exterior angles are congruent. Complementary angles sum to \(90^\circ\), supplementary to \(180^\circ\), and "not congruent" is incorrect here.

Step2: Evaluate Options

• Option A: Complementary is wrong.
• Option B: Supplementary is wrong.
• Option C: Not congruent is wrong.
• Option D: Congruent matches the theorem.

Step1: Recall Slope of Perpendicular Lines

If a line has slope \(m\), the slope of a line perpendicular to it is \(-\frac{1}{m}\) (negative reciprocal).

Step2: Find Slope of Given Line

The given line \(y = -5x + 6\) has slope \(m = -5\).

Step3: Calculate Perpendicular Slope

The negative reciprocal of \(-5\) is \(-\frac{1}{-5}=\frac{1}{5}\)? Wait, no: Wait, negative reciprocal of \(m\) is \(-\frac{1}{m}\). Wait, \(m = -5\), so \(-\frac{1}{m}=-\frac{1}{-5}=\frac{1}{5}\)? Wait, no, wait: Wait, perpendicular slope is negative reciprocal. So if \(m_1\) and \(m_2\) are perpendicular, \(m_1 \times m_2=-1\). So let \(m_2\) be the slope we need. Then \(-5 \times m_2=-1\), so \(m_2=\frac{-1}{-5}=\frac{1}{5}\)? Wait, no, wait: Wait, \(-5 \times m_2 = -1\) => \(m_2=\frac{-1}{-5}=\frac{1}{5}\)? Wait, no, \(-5 \times \frac{1}{5}=-1\), yes. Wait, the options: D is \(\frac{1}{5}\)? Wait, the options are A)5, B)\(-\frac{1}{5}\), C)\(-5\), D)\(\frac{1}{5}\). So yes, the slope is \(\frac{1}{5}\), which is option D.

Answer:

D) congruent.

Question 5