Discover what happens when three lines intersect to form a triangle, and explore the special angle relationships it creates.
When three lines intersect pairwise, they form a triangle. No matter its shape, the three interior angles of any triangle always add up to 180°.
A triangle has angles 50° and 70°. Find the third angle.
180° − 50° − 70° = 60°
A triangle has all three angles equal. What is each angle?
180° ÷ 3 = 60°
When one side of a triangle is extended, it forms an exterior angle. This exterior angle always equals the sum of the two interior angles that are not next to it.
A triangle has interior angles of 40° and 65° (not adjacent to the exterior angle). Find the exterior angle.
40° + 65° = 105°
An exterior angle of a triangle is 120°, and one of the non-adjacent interior angles is 50°. Find the other non-adjacent interior angle.
120° − 50° = 70°
1. A triangle has angles 45° and 85°. Find the third angle.
2. A triangle has two equal angles of 55° each. Find the third angle.
3. A triangle has interior angles of 35° and 80° (not adjacent to the exterior angle). Find the exterior angle.
4. An exterior angle of a triangle is 100°, and one non-adjacent interior angle is 45°. Find the other.
5. A triangle has one angle of 90°, and the other two are equal. Find those two angles.