Math Problem Statement
In ΔFGH, m∠F = (5x - 16)°, m∠G = (2x - 13)°, and m∠H = (8x + 14)°. Find m∠H.
Solution
Let's solve this step by step!
Problem:
We are given the angles of :
The sum of the interior angles of any triangle is .
So,
Step 1: Substitute the given expressions for the angles
Step 2: Simplify the equation
Combine like terms:
Step 3: Solve for
Add 15 to both sides: Divide both sides by 15:
Step 4: Find
Substitute into :
Final Answer:
Would you like further explanation or a breakdown of any specific step?
Here are 5 related questions to expand your understanding:
- What is the measure of and using ?
- How would you check your solution to ensure it satisfies the triangle's angle sum?
- Can you explain why the sum of interior angles in a triangle is always ?
- How would the problem change if one angle were an exterior angle?
- What if were negative—would it still produce valid triangle angles?
Tip: Always recheck your substitution to confirm accurate values for variables and expressions!
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Triangle Angle Sum Property
Formulas
Sum of angles in a triangle: m∠F + m∠G + m∠H = 180°
Theorems
Triangle Angle Sum Theorem
Suitable Grade Level
Grades 8-10