Alternate exterior angles are always congruent. If alternate exterior angles are congruent then lines are parallel. Alternate exterior angles are on the interior of two lines.
In the drawing below, angles 1 and 8 are alternate exterior angles, as are angles 2 and 7. Alternate exterior angles are congruent. Formally, alternate exterior angles are defined as two exterior angles on opposite sides of a transversal which lie on different parallel lines.
Also, do alternate exterior angles add up to 180? If the transversal cuts across parallel lines (the usual case) then exterior angles are supplementary (add to 180°). So in the figure above, as you move points A or B, the two angles shown always add to 180°. Try it and convince yourself this is true.
Keeping this in view, what can you say about alternate exterior angles?
The Alternate Exterior Angles Theorem states that if a pair of parallel lines are cut by a transversal, then the alternate exterior angles are congruent. Here we have a new pair of lines, parallel and crossed by a transversal.
Are alternate exterior angles complementary?
When the two lines intersected by the transversal are parallel, corresponding angles are congruent, alternate interior angles are congruent, alternate exterior angles are congruent, and consecutive interior angles become supplementary, which means they have a sum of 180 degrees.
What do alternate exterior angles look like?
Alternate exterior angles are angles that are on opposite sides of the transversal and outside the two lines. If the two lines are parallel, then the theorem tells you that the alternate exterior angles are congruent to each other.
What is alternate exterior angles Theorem?
The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate exterior angles are congruent .
How do you find the measure of exterior angles?
To find the value of a given exterior angle of a regular polygon, simply divide 360 by the number of sides or angles that the polygon has. For example, an eight-sided regular polygon, an octagon, has exterior angles that are 45 degrees each, because 360/8 = 45.
Which angles are congruent?
Congruent angles are two or more angles that have the same measure. In simple words, they have the same number of degrees. It’s important to note that the length of the angles’ edges or the direction of the angles has no effect on their congruency. As long as their measure is equal, the angles are considered congruent.
Are corresponding angles equal?
Corresponding Angles. When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles. When the two lines are parallel Corresponding Angles are equal.
Are parallel lines congruent?
If two parallel lines are cut by a transversal, the corresponding angles are congruent. If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel. Interior Angles on the Same Side of the Transversal: The name is a description of the “location” of the these angles.
Are vertical angles congruent?
When two lines intersect to make an X, angles on opposite sides of the X are called vertical angles. These angles are equal, and here’s the official theorem that tells you so. Vertical angles are congruent: If two angles are vertical angles, then they’re congruent (see the above figure).
Are same side exterior angles congruent?
Since alternate interior and alternate exterior angles are congruent and since linear pairs of angles are supplementary, same side angles are supplementary.
How do you solve for one side exterior angles?
Remember, when parallel lines are cut by a transversal line, same-side exterior angles are formed, which are outside of the parallel lines and on the same side of the transversal line. The theorem states that when parallel lines are cut by a transversal line, the same-side exterior angles are supplementary.
What are vertically opposite angles?
Vertically Opposite Angles. Vertically Opposite Angles are the angles opposite each other when two lines cross. “Vertical” in this case means they share the same Vertex (corner point), not the usual meaning of up-down.
What are the properties of alternate angles?
Alternate interior angles are formed when a transversal passes through two lines. The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles. The theorem says that when the lines are parallel, that the alternate interior angles are equal.