Can you construct a triangle all of whose angles are equal to 70°? If two of the angles are 70° what would the third angle be? If all the angles in a triangle have to be equal, then what must its measure be? Explore and find out.
Can a triangle with all angles = 70° be constructed?
Sum = 70° + 70° + 70° = 210° 210° 180° ∴ No, such a triangle cannot be constructed.
If two angles are 70° each, what is the third angle?
Third angle = 180° - 70° - 70° = 40° ∴ Third angle = 40°.
If all angles are equal, what must each measure be?
Let each angle = x x + x + x = 180° 3x = 180° x = 60° ∴ Each angle must be 60°.
Note: Such a triangle is called an equilateral triangle, where all sides are also equal.
Explanation
The chapter introduces the angle sum property: the sum of all three angles in a triangle is 180°. If two angles are 70° each, their sum is 140°, leaving only 40° for the third angle. For all angles to be equal, each must be 180°/3 = 60°. The chapter also mentions that equilateral triangles have all sides equal and all angles equal to 60°.
Solution Steps
If all angles = 70°, sum = 70° + 70° + 70° = 210° 180°
So such a triangle cannot exist
If two angles = 70°, third angle = 180° - 70° - 70° = 40°
For equal angles: let each = x, then 3x = 180°, so x = 60°