A convex polygon with 3 sides has angles 84 degrees, 2c degrees, and 2c degrees. What is the value of c?
Understand the Problem
The question is asking to find the value of c in a convex triangle where the angles are given as 84 degrees, 2c degrees, and 2c degrees. To solve this, we can use the fact that the sum of the angles in a triangle is equal to 180 degrees, and set up the equation: 84 + 2c + 2c = 180.
Answer
$c = 24$
Answer for screen readers
The value of $c$ is 24 degrees.
Steps to Solve
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Set Up the Equation We know the sum of the angles in a triangle is 180 degrees. Therefore, we can set up the equation: $$ 84 + 2c + 2c = 180 $$
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Combine Like Terms Combine the terms involving $c$: $$ 84 + 4c = 180 $$
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Isolate the Variable To isolate $c$, first subtract 84 from both sides: $$ 4c = 180 - 84 $$
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Calculate the Right Side Now perform the subtraction: $$ 4c = 96 $$
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Solve for c Finally, divide both sides by 4 to find the value of $c$: $$ c = \frac{96}{4} $$
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Final Calculation Calculating the division gives us: $$ c = 24 $$
The value of $c$ is 24 degrees.
More Information
In this problem, we applied the fundamental property of triangles where the sum of the interior angles equals 180 degrees. Identifying like terms and isolating the variable helped us find the solution systematically.
Tips
- Failing to combine like terms correctly can lead to incorrect results. Always ensure that terms are combined accurately.
- Forgetting to subtract or add the same value to both sides when isolating the variable can lead to errors. Remember to perform the same operation on both sides.
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