Find the interior angles formed at the intersection of two parallel secant lines. 1.The sum of two of them is 78 degrees.

Find the interior angles formed at the intersection of two parallel secant lines. 1.The sum of two of them is 78 degrees. 2. The difference between two of them is 16 degrees.

When two straight lines intersect, the inner angles are the angles: ∠3, ∠4, ∠5, ∠6.

The angle ∠3 is equal to the angle ∠6, and the angle ∠4 is equal to the angle ∠5, since these are cross-lying angles.

1)

Since the sum of the degree measures of two angles is 78º, it can only be the sum of the degree measures of the angles ∠4 and ∠5. Since these angles are equal, then:

∠4 = ∠5 = 78º / 2 = 39º.

The sum of the degree measures of the angles ∠3 and ∠4 is equal to 180º, since these angles are adjacent. Therefore:

∠3 = 180º – ∠4;

∠3 = 180º – 39º = 141º;

∠6 = ∠3 = 141º.

Answer: the interior angles ∠3 and ∠6 are equal to 141º, ∠4 and ∠5 are equal to 39º.

2)

Since the difference between the two angles is 16º, these angles are adjacent.

The sum of the degree measures of adjacent angles is 180 degrees, so we express:

x – degree measure of angle ∠4;

x + 16 – degree measure of angle ∠3;

x + x + 16 = 180;

x + x = 180 – 16;

2x = 164;

x = 164/2 = 82;

∠4 = 82º;

∠3 = 82º + 16º = 98º;

∠5 = ∠4 = 82º;

∠6 = ∠3 = 98º.

Answer: angles ∠5 and ∠4 are equal to 82º, angles ∠6 and ∠3 are equal to 98º.