The vertical angles add up to 88 degrees. Find the sum of the second pair of vertical angles

The vertical angles add up to 88 degrees. Find the sum of the second pair of vertical angles formed by the same straight lines.

Vertical angles are the angles formed by the intersection of two straight lines that have a common vertex and are located one opposite one. Their degree measures are equal:

∠1 = ∠3;

∠2 = ∠4.

The sum of the degree measures of all angles at the intersection of two straight lines is 360 °.

Since the sum of the degree measures of the angles ∠1 and ∠3 is 88 °, then:

∠1 = ∠3 = 88 ° / 2 = 44 °.

Thus, the sum of the degree measures of the angles ∠2 and ∠4 is equal to:

(∠2 + ∠4) = (360 ° – ∠1 – ∠3);

(∠2 + ∠4) = (360 ° – 44 ° – 44 °) = 272 °;

∠2 = ∠4 = 272 ° / 2 = 136 °.

Answer: the sum of the degree measures of the second pair of vertical angles is 272 °.