Triangle Properties

Triangles are fundamental shapes in geometry, and they have several unique properties that are crucial for solving SAT Math problems. The sum of the angles in any triangle is always equal to $180^{\circ}$. This property allows us to find unknown angles when at least one angle is known.

Example Problem

Find the measure of angle C in triangle ABC if angle A is $50^{\circ}$ and angle B is $70^{\circ}$.

1. Start with the formula for the sum of angles in a triangle: $$A + B + C = 180^{\circ}$$
2. Substitute the known values into the equation: $$50^{\circ} + 70^{\circ} + C = 180^{\circ}$$
3. Combine the angles on the left side: $$120^{\circ} + C = 180^{\circ}$$
4. Isolate $C$ by subtracting $120^{\circ}$ from both sides: $$C = 180^{\circ} - 120^{\circ}$$
5. Calculate the value of $C$: $$C = 60^{\circ}$$

Therefore, the measure of angle C is $60^{\circ}$.

Key Questions

• What is the sum of the interior angles of a triangle?
• If one angle of a triangle is $90^{\circ}$, what can you say about the other two angles?
• How do you calculate the third angle if two angles are known?
• What is the relationship between the sides of a triangle and its angles?

Keywords

• Triangle
• Angle
• Properties
• Sum of angles
• Interior angles