The first theorem
A ray has a start point and no end point. A ray starts at a point on a straight line. It makes two angles. What do they add to?
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- A straight line.
- A ray splits it into two angles.
- The first angle is 65°.
- The second is 115°. 65 + 115 = 180.
The rule
The two angles add to 180°.
An angle has a vertex (corner point) and two arms (sides). A linear pair is two angles sharing a vertex and an arm. Their other arms form a straight line.
Theorem. The two angles of a linear pair total 180°. A theorem is a fact we prove.
Why? Together they make a straight angle, the angle along a straight line. A straight angle is 180°. So the two parts add to 180°.
Example. One angle of a linear pair is 65°. The pair totals 180°. So the other is 180° − 65° = 115°.
Two names for totals. Angles that total 180° are supplementary, like 65° and 115°. Angles that total 90° are complementary.