If <2 = 3x -5 and <6 = 80x+20, how can we set up an equation that would help us solve for x?

Answer 1

You need to know something about the relationship between ∠2 and ∠6. They could be congruent (have the same measure) or be complementary (add up to a right angle, 90°) or supplementary (add up to the angle of at a point on a line). This will determine how you solve the problem.

If the angles are supplementary, 3x - 5 + 8x + 20 = 180, or 11x + 15 = 180, or 11x = 165, or x = 15, so the angles are 3(15) - 5 and 8(15) + 20 or 40 and 140; I'll bet this is the answer, just because textbooks like to have answers that are integers.

If the angles are congruent, 3x - 5 = 8x + 20, or 5x = -25, or x = -5, so the angle would be 3(-5) - 5 = -20. This would be a crazy answer.

If the angles are complementary, 3x - 5 + 8x + 20 = 90, or 11x + 15 = 90, or 11x = 75, or x = 75/11, so the angles are 3(75/11) - 5 and 8(75/11) + 20 or 170/11 and 820/11

Answer 2

You need to know the relationship between angle 2 and angle 6!

For example, maybe they are the base angles of an isosceles triangle.