Right Triangle Geometry: Finding the Sum of Non-Right Angles

Angle Sum Properties with Right Triangles

In a right triangle, the sum of the two non-right angles is...?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's find the sum of the non-right angles in a right triangle.
00:09 Label these angles as A and B.
00:16 Remember, the sum of all angles in a triangle is 180 degrees.
00:21 In a right triangle, one angle is 90 degrees, so A plus B equals 90 degrees.
00:34 And that's how you find their sum!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

In a right triangle, the sum of the two non-right angles is...?

2

Step-by-step solution

In a right-angled triangle, there is one angle that equals 90 degrees, and the other two angles sum up to 180 degrees (sum of angles in a triangle)

Therefore, the sum of the two non-right angles is 90 degrees

90+90=180 90+90=180

3

Final Answer

90 degrees

Key Points to Remember

Essential concepts to master this topic
  • Triangle Rule: All three angles in any triangle always sum to 180°
  • Technique: Subtract the right angle: 180° - 90° = 90°
  • Check: Add all angles: 90° + angle₁ + angle₂ = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Adding the right angle to find the sum
    Don't add 90° + (sum of other angles) = 180°! This confuses the total triangle sum with just the non-right angles. Always subtract the right angle from 180° to find what the other two must sum to.

Practice Quiz

Test your knowledge with interactive questions

Look at the angles shown in the figure below.

What is their relationship?

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FAQ

Everything you need to know about this question

Why do the other two angles have to add up to exactly 90°?

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Because every triangle's angles must sum to 180°. Since one angle is already 90°, the remaining two must add up to 180°90°=90° 180° - 90° = 90° to complete the triangle.

Can both non-right angles be equal?

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Yes! If both non-right angles are equal, each would be 45°. This creates a special right triangle called a 45-45-90 triangle or isosceles right triangle.

What if I'm given one of the non-right angles?

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Simply subtract it from 90°! For example, if one angle is 30°, the other must be 90°30°=60° 90° - 30° = 60° . The two non-right angles are complementary.

Does this rule work for all right triangles?

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Absolutely! Every right triangle, no matter its size or shape, follows this rule. The right angle is always 90°, so the other two always sum to 90°.

What's the difference between complementary and supplementary angles?

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Complementary angles add to 90° (like the non-right angles in a right triangle). Supplementary angles add to 180°. Remember: Complementary = Corner (90°)!

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