Use supplementary angles informally

Understands that adjacent angles forming a straight angle are supplementary and have measures totaling 180°, so the measure of one can be found by subtracting the other from 180°. Interprets this relationship in diagrams and real-world turns, distinguishing supplementary angles from complementary angles and from angles that merely share a vertex; this reasoning supports solving missing-angle problems and later formal angle relationships.

Detailed Explanation: Use supplementary angles informally

When two adjacent angles form a straight line, together they make a straight angle of $180^\circ$ . This means they are supplementary angles.

To find a missing angle:

Start with $180^\circ$ .
Subtract the angle you know.
Label the result with degrees.

Example: Angles $\angle AOB$ and $\angle BOC$ form a straight line. If $\angle AOB = 65^\circ$ , find $\angle BOC$ .

Since the angles form a straight line, their measures total $180^\circ$ :

65^\circ + \angle BOC = 180^\circ

Subtract $65^\circ$ from $180^\circ$ :

\angle BOC = 180^\circ - 65^\circ = 115^\circ

So, $\boxed{\angle BOC = 115^\circ}$ .

Remember: supplementary angles total $180^\circ$ . This is different from complementary angles, which total $90^\circ$ . Also, two angles that merely share a vertex are not necessarily supplementary; they must be adjacent and form a straight line.

Learn by doing: Use supplementary angles informally

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Geometry of Lines - Crossing Lines Solve Angle

Earned ?

Use supplementary angles informally

Detailed Explanation: Use supplementary angles informally

Learn by doing: Use supplementary angles informally

Practice with unlimited practice problems

Practice:

Geometry of Lines - Crossing Lines Solve Angle