How to find an unknown angle of a triangle?
Understand the Problem
The question is asking how to determine an unknown angle in a triangle, which typically involves using the properties of triangles, such as the sum of the internal angles being 180 degrees or applying trigonometric ratios if necessary.
Answer
The unknown angle is $70^\circ$.
Answer for screen readers
The unknown angle is $70^\circ$.
Steps to Solve
-
Identify Known Angles
List all the angles in the triangle that are already known. For example, if two angles are given as $40^\circ$ and $70^\circ$, write those values down. -
Use the Triangle Angle Sum Property
Recall that the sum of angles in a triangle is always $180^\circ$. Use this property to find the unknown angle.
For instance, if the known angles are $40^\circ$ and $70^\circ$, set up the equation:
$$ \text{Unknown Angle} + 40^\circ + 70^\circ = 180^\circ $$ -
Solve for the Unknown Angle
Rearranging the equation to solve for the unknown angle, you would subtract the known angles from $180^\circ$:
$$ \text{Unknown Angle} = 180^\circ - (40^\circ + 70^\circ) $$ -
Calculate the Unknown Angle
Perform the calculation:
$$ \text{Unknown Angle} = 180^\circ - 110^\circ = 70^\circ $$ -
Verify the Result
Double-check your work by ensuring that the sum of all angles equals $180^\circ$:
$$ 40^\circ + 70^\circ + 70^\circ = 180^\circ $$
The unknown angle is $70^\circ$.
More Information
In any triangle, the internal angles always add up to $180^\circ$. This fact is fundamental in geometry and is used frequently in solving triangle-related problems.
Tips
- Forgetting that the angles must sum to $180^\circ$; always check to ensure that all angles in the triangle have been accounted for.
- Miscalculating the sum of known angles, which can lead to an incorrect answer for the unknown angle.
