Digital SATMath: Geometry and TrigonometryEasy
A carpenter is cutting a triangular piece of wood for a roof truss. The triangle has angles measuring 35° and 75°. What is the measure of the third angle?
- A75°
- B35°
- C70°
- D110°
Show answer & explanationAnswer & explanation
Correct answer: C. 70°
The sum of the interior angles of any triangle is always 180°. Given two angles, the third angle can be found by subtracting the sum of the two known angles from 180°. 180° - (35° + 75°) = 180° - 110° = 70°.
Why the other options are wrong
- A. This would only be correct if the triangle was isosceles with the 75° angle repeating.
- B. This would only be correct if the triangle was isosceles with the 35° angle repeating.
- D. This is the sum of the two given angles, not the third angle.
Triangle Angle Sum Theorem
The sum of the measures of the interior angles of any triangle is always 180 degrees.
- Applies to all types of triangles (equilateral, isosceles, scalene).
- Used to find an unknown angle if two are known.
- Fundamental concept in Euclidean geometry.
Memory trick: Triangles always have angles that add to a straight line (180).