Right Angle Analysis: Examining Perpendicular Lines in a Complex Figure

Q: How can I be sure ALL angles are 90 degrees just by looking?

When the problem states all sides are perpendicular, this is a mathematical guarantee! Every intersection of perpendicular lines creates exactly $ 90° $ angles, regardless of how the shape looks.

Q: What if the shape looks like some angles are bigger or smaller?

This is a common visual illusion! Complex rectilinear shapes can trick your eyes, but mathematical definitions don't change. Perpendicular = $ 90° $ always.

Q: Are there any exceptions where perpendicular lines don't make 90° angles?

Never! By definition, perpendicular lines form right angles of exactly $ 90° $. If lines don't form $ 90° $ angles, they aren't perpendicular.

Q: How do I identify all the angles in this complex shape?

Look for each corner or intersection where two line segments meet. In this figure, there are 6 such points, and each one has a $ 90° $ angle.

Q: Could there be angles inside the shape that aren't 90 degrees?

No! The question asks about any angle in the drawing. Since all sides are perpendicular to each other, every angle formed where sides meet is exactly $ 90° $.

Perpendicular Lines with Complex Rectilinear Shapes

Given the figure in which all sides are perpendicular to each other, is there any angle in the drawing that is not equal to 90 degrees?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Is there a non-right angle in the drawing?

00:03 All sides are perpendicular to each other according to the given data

00:06 Let's mark all our angles

00:13 All our angles are right angles

00:17 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the figure in which all sides are perpendicular to each other, is there any angle in the drawing that is not equal to 90 degrees?

Step-by-step solution

Let's remember that perpendicular sides create a 90-degree angle between them.

We will draw a 90-degree angle at each intersection of the sides as follows:

From the figure, we notice that there is not a single angle that is not right.

Final Answer

False

Key Points to Remember

Essential concepts to master this topic

Definition: Perpendicular lines always form 90-degree right angles
Technique: Mark each corner with right angle symbol (□) = 90°
Check: Count all angles in figure - if all perpendicular, all equal 90° ✓

Common Mistakes

Avoid these frequent errors

Assuming interior angles might be different from 90 degrees
Don't think some angles look different just because the shape is complex = wrong conclusions about angle measures! Visual perception can be misleading in rectilinear figures. Always remember that perpendicular means exactly 90 degrees at every single intersection.

Practice Quiz

Test your knowledge with interactive questions

What do the four figures below have in common?

FAQ

Everything you need to know about this question

How can I be sure ALL angles are 90 degrees just by looking?

When the problem states all sides are perpendicular, this is a mathematical guarantee! Every intersection of perpendicular lines creates exactly $90°$ angles, regardless of how the shape looks.

What if the shape looks like some angles are bigger or smaller?

This is a common visual illusion! Complex rectilinear shapes can trick your eyes, but mathematical definitions don't change. Perpendicular = $90°$ always.

Are there any exceptions where perpendicular lines don't make 90° angles?

Never! By definition, perpendicular lines form right angles of exactly $90°$ . If lines don't form $90°$ angles, they aren't perpendicular.

How do I identify all the angles in this complex shape?

Look for each corner or intersection where two line segments meet. In this figure, there are 6 such points, and each one has a $90°$ angle.

Could there be angles inside the shape that aren't 90 degrees?

No! The question asks about any angle in the drawing. Since all sides are perpendicular to each other, every angle formed where sides meet is exactly $90°$ .

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