Question

1 multiple choice 1 point
if ( mangle cjk ) is ( 75^{circ} ), what is ( mangle dkl )?

2 multiple choice 1 point
which is an equation of a line that is perpendicular to the line whose equation is ( y=\frac{1}{3}x - 2 )?

Explanation:

Step1: Identify the relationship between angles

Since \(AF\parallel HL\) (assumed from the figure structure), and \(BE\) is a transversal. \(\angleCJK\) and \(\angleDKL\) are corresponding angles.

Step2: Use the property of corresponding angles

When two parallel lines are cut by a transversal, corresponding angles are equal. Given \(m\angleCJK = 75^{\circ}\), so \(m\angleDKL=m\angleCJK\)

for the second question:

Step1: Recall the slope - perpendicular line relationship

The equation of a line is in the form \(y = mx + b\), where \(m\) is the slope. If a line has a slope \(m_1\), a line perpendicular to it has a slope \(m_2\) such that \(m_1\times m_2=- 1\). For the line \(y=\frac{1}{3}x - 2\), \(m_1=\frac{1}{3}\). Let the slope of the perpendicular line be \(m_2\). Then \(\frac{1}{3}\times m_2=-1\), solving for \(m_2\) gives \(m_2=-3\)

Answer:

\(75^{\circ}\)