Question

15 POINTS: The ratio of the same side interior angles of two parallel lines is 33:3. Find the measures of all eight angles formed by the parallel lines and transversal.

Answer 1

Answer:

$15^\circ,165^\circ,15^\circ,165^\circ\\15^\circ,165^\circ,15^\circ,165^\circ$

Step-by-step explanation:

The ratio of the same side interior angles of two parallel lines is 33:3

If two parallel lines are cut by a transversal

Sum of the same side interior angles = 180 degrees.

Therefore, the two same-side interior angles are:  

$\dfrac{33}{36}\times 180^\circ =165^\circ\\\dfrac{3}{36}\times 180^\circ =15^\circ$

We can then say that the measure of all eight angles formed by the parallel lines and transversal starting from the upper left in a clockwise rotation is:

$15^\circ,165^\circ,15^\circ,165^\circ, 15^\circ,165^\circ,15^\circ,165^\circ$