Answer:
The measures of all eight angles formed by the parallel lines and transversal are;
The four angles for the one of the parallel line = 12°, 168°, 12°, 168°
The four angles for the other parallel line = 12°, 168°, 12°, 168°
Step-by-step explanation:
The same-side interior angle theorem states that the the sum of the same side interior angles formed by the transversal intersection of two parallel lines is equal to 180°
Whereby the ratio of the angles is 1:14, we have;
Let one of the angles = x
Therefore, the other angle = 14·x
We then have;
x + 14·x = 180°
15·x = 180°
x = 180°/15 = 12°
∴ The other angle = 14×12 = 168°
Hence the four angles on one of the parallel lines are therefore;
12°, 168°, 12°, 168°
Similarly, the four angles on one of the other parallel line are;
12°, 168°, 12°, 168°
The measures of all eight angles formed by the parallel lines and transversal = 12°, 12°, 12°, 12°, 168°, 168°, 168°, 168°.
