Two angles of a triangle are 50 and 130. What is the third?
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Step-by-Step Solution
Step 1: Recall the Angle Sum Property of a Triangle
The Angle Sum Property of a Triangle states that the sum of the interior angles of any triangle is always equal to 180∘. This is a fundamental property of Euclidean geometry.
Step 2: Substitute the given angles
We are given two angles of the triangle as 50∘ and 130∘. Let's substitute these values into the Angle Sum Property equation, where C represents the unknown third angle.
Step 3: Calculate the sum of the known angles
First, we add the two known angles together: 50∘+130∘=180∘. This simplifies our equation, making it easier to solve for the third angle.
Step 4: Solve for the third angle
To find the third angle C, we subtract the sum of the known angles (180∘) from the total sum of angles in a triangle (180∘). This gives us the measure of the missing angle.
Step 5: Interpret the result
A triangle cannot have an angle of 0∘. This result indicates that a triangle with angles 50∘ and 130∘ cannot exist. The sum of two angles is already 180∘, which means the third angle would have to be 0∘, making it a degenerate triangle (a straight line).