Math Problem Statement
Solution
The diagram you uploaded shows several angles formed by intersecting lines. We are tasked with finding the missing angles and .
Step-by-step solution:
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Identify known angles and relationships:
- The diagram shows a 90° angle in the lower-right quadrant, which splits the vertical and horizontal lines.
- The angle labeled 38° shares a straight line with angle , meaning these two angles are supplementary. So, .
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Find angle : Using the supplementary angle relationship:
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Find angle : The sum of the angles around the point where and the 90° angle meet must equal 180° because they form a straight line. Solving for :
Final Answer:
Would you like further clarification on these steps or more detailed explanations?
Here are 5 related questions for practice:
- If an angle is complementary to , what is its measure?
- What would the measure of be if the angle adjacent to it was 40° instead of 38°?
- What are supplementary angles, and why are and 38° supplementary?
- If the angle was bisected, what would each smaller angle measure?
- Can a right angle ever be supplementary? Explain why or why not.
Tip: Remember that supplementary angles always add up to 180°, while complementary angles sum to 90°.
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Math Problem Analysis
Mathematical Concepts
Geometry
Supplementary Angles
Right Angles
Formulas
x + 38° = 180°
y + 90° = 180°
Theorems
Supplementary Angles Theorem
Right Angle Theorem
Suitable Grade Level
Grades 6-8