Find the Missing Angle: 120-Degree Geometric Construction Problem

Rectangle Angle Properties with External Extensions

Calculate the missing angle:

120120120

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Step-by-step written solution

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1

Understand the problem

Calculate the missing angle:

120120120

2

Step-by-step solution

In this question, we are asked to find the measure of the angle marked in orange.

We can see that it is adjacent to the left vertex of the rectangle, and its sides are extensions of the rectangle’s sides. This means that the angle is directly opposite the rectangle’s vertex, where a right angle is formed.

Since all angles in a rectangle measure 90∘90∘, the angle we were asked to find is also equal to 90∘90∘.

3

Final Answer

90

Key Points to Remember

Essential concepts to master this topic
  • Rectangle Property: All internal angles in rectangles measure exactly 90°
  • External Extension: Orange angle shares vertex with rectangle's 90° corner
  • Verification: Adjacent angles at rectangle vertex always sum to 90° ✓

Common Mistakes

Avoid these frequent errors
  • Assuming the 120° angle affects the missing angle
    Don't use the 120° diagonal angle to calculate the orange angle = wrong answer! The 120° is on a diagonal line, not related to the rectangle's corner angles. Always focus on the rectangle's vertex properties where perpendicular sides create 90° angles.

Practice Quiz

Test your knowledge with interactive questions

If one of two corresponding angles is a right angle, then the other angle will also be a right angle.

FAQ

Everything you need to know about this question

Why doesn't the 120° angle matter for finding the missing angle?

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The 120° angle is on a diagonal line that crosses the rectangle, but the orange angle is formed by extensions of the rectangle's sides. These are completely separate geometric relationships!

How do I know this angle is exactly 90°?

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The orange angle shares the same vertex as the rectangle's corner. Since rectangles have perpendicular sides, any angle formed by extending those sides will also be 90°.

What if the rectangle was tilted or rotated?

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It doesn't matter! A rectangle's internal angles are always 90° regardless of its position. The angle formed by extending perpendicular sides will always be 90°.

Could this angle be different if the sides were longer or shorter?

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No! The length of the sides doesn't affect the angle measure. As long as the sides are perpendicular (which they are in rectangles), the angle will always be 90°.

How can I double-check this is really 90°?

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Look for the small square symbol at the rectangle's corner - this indicates a right angle. Since the orange angle uses the same vertex and sides, it must also be 90°!

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