Math Problem Statement
Solution
Let's analyze the image step by step to find the missing angles, and .
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Understanding the setup:
- The diagram shows multiple lines intersecting at a point.
- One of the given angles is , and we are asked to find the angles and .
- There is also a right angle formed by two perpendicular lines, which will help in solving the angles.
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Applying the straight angle property:
- A straight angle measures , so the total of angles around a straight line must equal .
- The angle adjacent to , which includes the angle , forms a straight line. Therefore, .
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Using the right angle to find :
- We know there is a right angle where the line containing meets the horizontal line, so the total of the angles around this point must equal . Since , the remaining part forms a vertical line perpendicular to the horizontal line.
The sum of angles around a point is , so:
Solving for :
Final Answers:
Would you like more details on the calculation or a breakdown of the concepts?
Here are five follow-up questions based on this problem:
- What is the sum of the angles around a point?
- How do you calculate the missing angle when you have a straight line?
- What is the measure of a right angle in degrees?
- Why is equal to 180° in this context?
- Can you find the value of angle if angle were different?
Tip: When solving for angles in geometry, always look for straight lines (180°) and right angles (90°) to help determine unknown values.
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Math Problem Analysis
Mathematical Concepts
Geometry
Angle Relationships
Straight Angles
Right Angles
Formulas
x + 33° = 180° (Straight angle)
y + 90° + 33° = 180° (Angles around a point)
Theorems
The sum of angles around a straight line is 180°
The sum of angles around a point is 360°
Right angle = 90°
Suitable Grade Level
Grades 7-9
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