Question

two lines parallel to the same line are parallel
determined the measures h and k.

Explanation:

Step1: Analyze the parallel lines and angles

Assuming \( \ell_1 \parallel \ell_2 \), we can use properties of parallel lines (corresponding angles, alternate interior angles) and triangle angle - sum (if applicable). Let's assume the triangle formed has some isosceles properties (from the markings, maybe the triangle with side \( h \) has equal sides). Also, using the angle of \( 48^\circ \) (from the diagram, alternate interior angles or corresponding angles).

Step2: Determine \( h \)

If we consider the triangle with angle \( 48^\circ \) and the fact that lines are parallel, maybe \( h = 48^\circ \) (using alternate interior angles or isosceles triangle properties, since the sides are marked equal, so the base angles are equal).

Step3: Determine \( k \)

Since \( \ell_1 \parallel \ell_2 \), and using the property of parallel lines and transversals, \( k \) should be equal to the angle that is alternate interior or corresponding to the \( 48^\circ \) angle? Wait, maybe \( k = 48^\circ \) as well? Wait, no, maybe there is a different approach. Wait, if the triangle is isosceles with two equal sides (marked with the same tick marks), then the base angles are equal. If one angle is related to the parallel lines, let's re - evaluate.

Wait, perhaps the angle \( h \) is equal to \( 48^\circ \) because of alternate interior angles (since the lines are parallel) and \( k \) is also \( 48^\circ \) due to the same parallel line properties (corresponding angles).

Answer:

\( h = 48^\circ \), \( k = 48^\circ \) (Note: The answer depends on the exact diagram markings. If the triangle is isosceles and lines are parallel, this is a possible solution. If there are more details, the answer may vary, but with the given information, this is a reasonable assumption based on parallel line and triangle angle properties.)