solve this---Problem Number: 32
Chart/Diagram Description:
* Type: Geometric figure (triangle).
* Main Elements: A triangle with three vertices and three sides. The interior angles are labeled as a°, b°, and c°.
* Annotation: A note below the triangle states "Note: Figure not drawn to scale."
Textual Information:
* Question Stem: In the triangle above, a = 34. What is the value of b + c?
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In this problem, we have a triangle with interior angles labeled as a degrees, b degrees, and c degrees. We're told that angle a equals 34 degrees, and we need to find the value of b plus c. Let's start by recalling what we know about the interior angles of a triangle.
A fundamental property of triangles is that the sum of all interior angles is always 180 degrees. This is true for any triangle, regardless of its shape or size. So we can write the equation: a plus b plus c equals 180 degrees. We're given that angle a equals 34 degrees. Let's substitute this value into our equation.
Now, let's substitute the known value of a equals 34 degrees into our equation. We have 34 degrees plus b plus c equals 180 degrees. To find b plus c, we need to isolate these terms on one side of the equation. We can subtract 34 degrees from both sides. This gives us b plus c equals 180 degrees minus 34 degrees, which equals 146 degrees.
Therefore, the value of b plus c equals 146 degrees. This is our final answer. To summarize our solution: We started with the fact that the sum of interior angles in any triangle is 180 degrees. We were given that angle a equals 34 degrees. By substituting this value into the equation a plus b plus c equals 180 degrees, we found that b plus c equals 146 degrees.
Let's summarize what we've learned. First, the sum of interior angles in any triangle is always 180 degrees. This is a fundamental property of triangles. Second, when one angle is known, we can find the sum of the other two angles by subtracting the known angle from 180 degrees. In our problem, since angle a equals 34 degrees, the sum of angles b and c equals 146 degrees. This principle applies to all triangles, regardless of their shape or size.