Math Problem Statement
Determine the values of the unknown angles in the given diagrams.
Solution
The image you've uploaded contains a set of geometry problems involving angle properties. Let's go through each part to determine the unknown angles:
a) Triangle with angles , , and :
- You know that one angle is .
- In any triangle, the sum of the internal angles is . Therefore, if one angle is , and if and are the other two angles, we can solve for the unknowns:
b) Adjacent Angles with the angle and :
- Since the angles on a straight line sum to , we can subtract the known angles from to find the unknown angle:
c) Triangle with and angles:
- Again, using the fact that the sum of the angles in any triangle is , we can determine the unknown angle:
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Math Problem Analysis
Mathematical Concepts
Triangle Angle Sum
Linear Pair of Angles
Parallel Lines and Transversals
Formulas
Sum of interior angles in a triangle: a + b + c = 180°
Supplementary angles: a + b = 180°
Theorems
Triangle Sum Theorem
Linear Pair Theorem
Alternate Interior Angles Theorem
Suitable Grade Level
Grades 7-9