Math Problem Statement
Solution
To solve this problem, we need to determine the value of and find the measures of the angles in the triangle .
Since is a triangle, the sum of its interior angles must equal .
The angles are given as follows:
Step 1: Set up the equation
Using the triangle angle sum property:
Step 2: Simplify the equation
Combine like terms:
Step 3: Solve for
Subtract 24 from both sides:
Now, divide by 4:
Step 4: Substitute back to find the angles
Now that we know , we can substitute this value into each angle expression to find their measures.
Final Answer:
Would you like further explanation or have any other questions?
Here are five related questions to deepen understanding:
- What is the triangle angle sum property, and why does it hold?
- How can we verify the values of and the angles we found?
- What would change if the triangle were not a standard triangle but an isosceles or equilateral triangle?
- How do supplementary angles relate to solving for angles in triangles?
- What other geometric shapes have specific angle sum properties?
Tip: When solving for unknowns in geometric figures, always start by applying known properties like the angle sum for triangles or polygons. This ensures that your setup is grounded in a fundamental rule.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Geometry
Triangle Properties
Algebra
Formulas
Sum of interior angles of a triangle = 180°
Theorems
Triangle Angle Sum Theorem
Suitable Grade Level
Grades 8-10