Answer:
x = 145
Step-by-step explanation:
You want the value of x given that x° and 35° are consecutive interior angles at parallel lines.
Transversal
The one line (t) crossing the two parallel lines (m and n) is called a "transversal." At each intersection, it creates four (4) angles. When the lines are parallel, the four angles at one intersection are identical in value to the four corresponding angles at the other intersection.
Various names are given to pairs of these angles.
Angle naming
Angles not between the parallel lines are called "exterior" angles. Those that are between the parallel lines are called "interior" angles.
Angles that lie in the same direction from the points where the lines intersect are called "corresponding" angles. For example, the angle above and adjacent to angle x° corresponds to the angle marked 35°.
Angles on the same side of the transversal are "same-side" or "consecutive" angles. The marked angles x° and 35° are consecutive interior angles.
Angles on opposite sides of the transversal are called "alternate" angles.
Angle relations
A number of theorems describe the relationship between various angles in this parallel-line geometry. The upshot is that all four of the obtuse angles are congruent, and all four of the acute angles are congruent. If the transversal crosses at right angles, then all 8 right angles are congruent.
The theorems might be named ...
- corresponding angles theorem — corresponding angles are congruent
- alternate exterior angles theorem — alternate exterior angles are congruent
- alternate interior angles theorem — alternate interior angles are congruent
- consecutive exterior angles theorem — consecutive exterior angles are supplementary
- consecutive interior angles theorem — consecutive interior angles are supplementary
Of course, the usual relations where one line crosses another also apply:
- vertical angles are congruent
- angles of a linear pair are supplementary
Given angles
By now, you know the marked angles are "same-side interior angles". These consecutive interior angles are supplementary, so ...
x° +35° = 180°
x = 180 -35 = 145
The value of x is 145.
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Additional comment
It is a good idea to learn this vocabulary and the various angle relations. You will see it again.
The converse of each of these theorems is also true. If the angles have the specified relationship, then the lines are parallel.
