Find all the angles formed at the intersection of two parallel secant lines if one of them is 42 °.

According to the theorem on the intersection of parallel secant lines, the corresponding angles formed are equal to:

∠1 = ∠5;

∠2 = ∠6;

∠3 = ∠7;

∠4 = ∠8.

Since the sum of one-sided angles at the intersection of parallel straight lines is 180º, and the angle ∠1 is 42º:

∠1 + ∠2 = 180º

∠2 = 180º – ∠1;

∠2 = 180º – 42º = 138º.

Thus:

∠5 = ∠1 = 42º;

∠6 = ∠2 = 138º.

When intersecting parallel straight lines, the intersecting angles are also equal:

∠8 = ∠1 = 42º;

∠7 = ∠2 = 138º;

∠6 = ∠3 = 138º;

∠5 = ∠4 = 42º.

Answer: ∠1 = ∠4 = ∠5 = ∠8 = 42º, ∠2 = ∠3 = ∠6 = ∠7 = 138º.