What is an angle in geometry?

An angle is formed when two rays share a common endpoint, called the vertex. It is measured in degrees.

Define complementary angles.

Complementary angles are two angles whose measures add up to 90 degrees. For example, if one angle measures 30 degrees, the other must measure 60 degrees.

Define supplementary angles.

Supplementary angles are two angles whose measures add up to 180 degrees. For instance, if one angle is 110 degrees, the other must be 70 degrees.

What are vertically opposite angles?

When two lines intersect, they form two pairs of vertically opposite angles, which are always equal in measure.

What is a transversal?

A transversal is a line that crosses two or more lines at distinct points, creating various angles.

What are corresponding angles?

Corresponding angles are pairs of angles that lie on the same side of the transversal and in corresponding positions relative to the two lines. They are equal when the lines are parallel.

State the formula for the sum of angles on a straight line.

The sum of all angles on one side of a straight line is always 180 degrees.

What are alternate interior angles?

Alternate interior angles are pairs of angles that lie on opposite sides of the transversal and inside the two lines. They are equal when the lines are parallel.

What is the relationship between interior and exterior angles?

Interior angles are those between two lines, while exterior angles are outside. The sum of an interior angle and its corresponding exterior angle is 180 degrees.

If angle A measures 2x + 10 and angle B measures x + 50, and they are supplementary, find x.

Hint: Set up the equation (2x + 10) + (x + 50) = 180.

Combine the angles: 2x + 10 + x + 50 = 180 simplifies to 3x + 60 = 180. Subtract 60 from both sides: 3x = 120. Divide by 3: x = 40.

What is the measure of a straight angle?

A straight angle measures exactly 180 degrees.

If two parallel lines are cut by a transversal, what can be said about alternate exterior angles?

Alternate exterior angles are equal when two parallel lines are cut by a transversal.

What is the formula for the sum of angles around a point?

The sum of all angles around a point is always 360 degrees.

If two angles are complementary and one angle measures 30 degrees, what is the measure of the other angle?

The other angle measures 60 degrees since 30 + 60 = 90.

What is a right angle?

A right angle measures exactly 90 degrees.

If angle C is a reflex angle, what is its range of measurement?

A reflex angle measures between 180 degrees and 360 degrees.

What is the relationship between angles formed by two intersecting lines?

The angles formed are vertically opposite, adjacent, and linear pairs; vertically opposite angles are equal, and adjacent angles are supplementary.

How can you identify if two lines are parallel using angles?

If corresponding angles are equal or alternate interior angles are equal when a transversal crosses the lines, then the lines are parallel.

What is the definition of a line segment?

A line segment is a part of a line that has two endpoints.

What is a linear pair of angles?

A linear pair of angles are two adjacent angles that form a straight line, summing up to 180 degrees.