Math Problem Statement
find x
Solution
To solve the problem, we need to find the angle . Let's analyze the given figure step by step.
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Identify the known angles:
- The angle adjacent to the 125° angle in the first square is 40°.
- The angle adjacent to the 125° angle in the second square is 35°.
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Identify the properties of squares:
- All angles inside each square are 90°.
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Using the properties of the angles around a point:
- The sum of angles around a point is 360°.
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Determine the sum of angles around the point where all squares meet:
- (given)
- (given)
- (from the square on the top)
- (given)
- (from the square at the bottom)
The equation will be:
Simplifying:
However, we need to subtract an extra 20° as an external angle, so we consider only internal angles, leading us to:
So, considering all angles together (there's a mistake earlier because the sum should always be ), so here we correctly calculate:
So, angle is .
Thus, the correct answer is (b) .
Would you like further details or have any questions?
Here are some related questions:
- How do we calculate angles around a point?
- What properties do quadrilaterals have?
- Why is the sum of angles around a point always 360°?
- How would the problem change if one of the quadrilaterals wasn't a square?
- Can you explain external and internal angles in polygons?
- What would the solution be if all given angles were external angles?
- How do square properties affect angle calculation?
- What methods can we use to confirm the solution is correct?
Tip: Always verify your angle summations with geometric rules to avoid errors in complex figures!
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Math Problem Analysis
Mathematical Concepts
Geometry
Angles
Properties of Squares
Formulas
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Theorems
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Suitable Grade Level
High School
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