Math Problem Statement
solve
Find angle A in a triangle where one angle is 60 degrees, another angle is (x + 54) degrees, and the third angle is (84 + x) degrees.
Solution
To solve for in the given triangle, we can use the triangle angle sum property, which states that the sum of the angles in any triangle is .
The three angles in the triangle are:
- (at vertex ),
- (adjacent to vertex ),
- .
The sum of the angles is:
Now, let's solve for .
Now, substitute into the expression for :
Thus, .
Would you like more details or have any other questions?
Here are 5 related questions:
- How can you confirm the solution by checking all angles of the triangle?
- How does the triangle angle sum property apply to different types of triangles?
- What would happen if had a different expression? How would that change the solution?
- Can you solve for the other two angles of the triangle?
- What is the relationship between this method and the exterior angle theorem?
Tip: Always ensure the total sum of interior angles of a triangle equals when verifying solutions.
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Math Problem Analysis
Mathematical Concepts
Geometry
Triangle Angle Sum Property
Formulas
Sum of angles in a triangle = 180°
Theorems
Triangle Angle Sum Theorem
Suitable Grade Level
Grades 8-10