Geometry / Unit 5: Congruent Triangles
5.1 Triangle Angle Sum and Exterior Angles
Notes
The angles of every triangle add to $180^\circ$.
- Triangle Angle Sum Theorem: $m\angle A + m\angle B + m\angle C = 180^\circ$.
- An exterior angle is formed by one side and the extension of another side.
- Exterior Angle Theorem: an exterior angle equals the sum of the two remote (nonadjacent) interior angles.
- The acute angles of a right triangle are complementary.
- Example: interior angles $50^\circ$ and $60^\circ$ make the third angle $70^\circ$, and the exterior angle at that vertex $110^\circ$.
Practice
In $\triangle ABC$, $m\angle A = 47^\circ$ and $m\angle B = 68^\circ$. Find $m\angle C$.
$180 - 47 - 68 = 65$.
In $\triangle PQR$, the exterior angle at $R$ measures $125^\circ$ and $m\angle P = 70^\circ$. Find $m\angle Q$.
Exterior angle $= m\angle P + m\angle Q$, so $125 = 70 + m\angle Q$.
The angles of a triangle measure $x^\circ$, $2x^\circ$ and $3x^\circ$. What is the largest angle?
$6x = 180$, so $x = 30$ and $3x = 90$.
Ready for more? Take the Unit 5 test.