Right Triangle Angles: Finding Two Missing Interior Angles

Triangle Angle Properties with Right Angle Classification

Does every right triangle have an angle _____ The other two angles are _______

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Fill in the missing values
00:05 Draw a right triangle
00:12 Mark the remaining angles with letters A,B
00:19 The sum of angles in a triangle equals 180
00:29 Isolate the sum of the remaining angles
00:35 From the equation we can conclude that every second angle is less than 90 (acute)
00:48 Therefore in a right triangle there is one right angle and the rest are acute
00:51 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Does every right triangle have an angle _____ The other two angles are _______

2

Step-by-step solution

Let's analyze the problem to understand how the angles are defined in a right triangle.

A right triangle is defined as a triangle that has one angle equal to 9090^\circ. This is known as a right angle. Because the sum of all angles in any triangle must be 180180^\circ, the two remaining angles must add up to 9090^\circ (i.e., 18090180^\circ - 90^\circ).

In a right triangle, the right angle is always present, leaving the other two angles to be less than 9090^\circ each. These angles are called acute angles. An acute angle is an angle that is less than 9090^\circ.

To summarize, the angle types in a right triangle are:

  • One angle that is 9090^\circ (a right angle).
  • Two angles that are each less than 9090^\circ (acute angles).

Given the choices, the description "Straight, sharp" correlates to the angle types in a right triangle, as "Straight" can be associated with the 9090^\circ angle (though it's generally called a right angle) and "Sharp" correlates with acute angles.

Therefore, the correct aspect of the other two angles in a right triangle are straight (right) and sharp (acute), which matches the correct choice.

Therefore, the solution to the problem is Straight, sharp.

3

Final Answer

Straight, sharp

Key Points to Remember

Essential concepts to master this topic
  • Rule: Right triangles have one 90° angle and two acute angles
  • Technique: Use angle sum property: 180° - 90° = 90° for remaining angles
  • Check: All three angles add to exactly 180° in any triangle ✓

Common Mistakes

Avoid these frequent errors
  • Confusing angle terminology and types
    Don't mix up 'straight angle' (180°) with 'right angle' (90°) = wrong classifications! A straight angle is a completely different concept. Always remember: right triangles have ONE right angle (90°) and TWO acute angles (less than 90° each).

Practice Quiz

Test your knowledge with interactive questions

In a right triangle, the side opposite the right angle is called....?

FAQ

Everything you need to know about this question

What's the difference between a right angle and a straight angle?

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A right angle measures exactly 9090^\circ and forms a perfect corner (like the corner of a square). A straight angle measures 180180^\circ and forms a straight line. In triangles, we only deal with right angles!

Why are the other two angles called 'acute' or 'sharp'?

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Acute angles are less than 9090^\circ and look 'sharp' or pointed. Since the two non-right angles in a right triangle must add up to 9090^\circ, each one must be less than 9090^\circ, making them acute!

Can a right triangle have two 90° angles?

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No! If two angles were 9090^\circ each, they'd already add up to 180180^\circ, leaving no room for a third angle. Remember: all triangle angles must sum to exactly 180180^\circ.

How do I remember which angles are which in a right triangle?

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Think of it this way: Right triangles are 'right' because they have exactly ONE right angle. The other two angles are always smaller (acute) because they have to share the remaining 9090^\circ between them!

What if the problem uses different terminology like 'straight' and 'sharp'?

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Some problems use informal terms: 'straight' often refers to the right angle (though this can be confusing), and 'sharp' refers to acute angles. Always focus on the actual angle measurements: one 9090^\circ and two less than 9090^\circ.

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