Lesson 8: Angles, Lines, and Transversals

Property

When a transversal intersects two parallel lines, corresponding angles are congruent. Corresponding angles occupy the same relative position at each intersection point.

Examples

Property

• The sum of the measures of interior angles in a triangle is $180^\circ$.
• Vertical angles have equal measure.
• Complementary angles add up to $90^\circ$.
• Supplementary angles add up to $180^\circ$.

The use of algebraic language can help us to write relationships and solve problems.

Examples

• Two angles lie on a straight line. One is $115^\circ$ and the other is $x$. Since they are supplementary, their sum is $180^\circ$. The equation is $x + 115 = 180$, so $x = 65^\circ$.
• The angles in a triangle are $x$, $2x$, and $60^\circ$. They must sum to $180^\circ$, so $x + 2x + 60 = 180$. This gives $3x = 120$, so $x = 40^\circ$. The angles are $40^\circ$, $80^\circ$, and $60^\circ$.
• An angle of $50^\circ$ and an angle of $y$ are complementary. This means their sum is $90^\circ$. The equation is $50 + y = 90$, so the unknown angle $y$ is $40^\circ$.

Explanation

Geometric rules about angles are like secret codes for making equations. If you know angles add up to $180^\circ$ or are equal, you can set up a problem to find the missing piece, $x$.