How to find angles of a triangle with one angle?

Understand the Problem

The question is asking how to determine the angles of a triangle when one angle is known. In a triangle, the sum of all three angles is always 180 degrees, so if one angle is known, the other two can be found by subtracting the known angle from 180 degrees and applying the properties of triangles.

Answer

If $A$ is known, then $B + C = 180^\circ - A$. In an isosceles triangle, $B = C = \frac{180^\circ - A}{2}$.

Steps to Solve

Identify the known angle

Let’s denote the known angle as $A$. Make sure you have the measure of angle $A$ in degrees.

Calculate the remaining sum of angles

Since the sum of all angles in a triangle is 180 degrees, the sum of the other two angles, $B$ and $C$, can be calculated as follows:

$$ B + C = 180^\circ - A $$

Use the properties of the triangle

Sometimes, additional information about the triangle (like being an isosceles or right triangle) might help you find exact measures for angles $B$ and $C$. For example, if the triangle is isosceles and $A$ is the unique angle, then:

$$ B = C = \frac{180^\circ - A}{2} $$

Final step: Assign values to the angles

Use the equations from the previous steps to find the measures of angles $B$ and $C$. Depending on the nature of the triangle, plug in values accordingly.

The measures of angles $B$ and $C$ can be determined as follows:

If $A$ is known, then:

$$ B + C = 180^\circ - A $$

If it's an isosceles triangle with $B = C$, then:

$$ B = C = \frac{180^\circ - A}{2} $$

More Information

In any triangle, the sum of its interior angles always equals 180 degrees. This property is crucial for solving for unknown angles. In special cases like isosceles triangles, angle measures can be inferred even more easily.

Tips

Forgetting that the sum of angles in a triangle is 180 degrees can lead to incorrect calculations.
Assuming equal angles in an isosceles triangle without confirming which angles are equal.

Thank you for voting!