I’m confused on the type of angles these are and how to solve them . (parallel lines and transversals)

7) 49°

8) 77°

9) 87°

10) 135°

Step-by-step explanation:

7) The angles are between the parallel lines, so are "interior." They are on opposite sides of the transversal, so are "opposite interior" angles. Such angles are congruent, so ...

... ? ≅ 49°

8) The angles are adjacent interior angles, so are supplementary.

... ? + 103° = 180°

... ? = 77°

9) The angles are outside the parallel lines, so are "exterior." They are on opposite sides of the transversal, so are "opposite exterior" angles. Such angles are congruent.

... ? ≅ 87°

10) These are vertical angles, so are congruent. (The other parallel line is irrelevant and doesn't need to be there for this relationship to be true.)

... ? ≅ 135°

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11