Find the Angles in an Isosceles Right Triangle: 90-Degree Corner Analysis

Triangle Angle Properties with Equal Sides

Look at the isosceles right-angled triangle below.

Calculate its angles.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the angles of the triangle
00:03 The sum of the angles in a triangle equals 180
00:07 Given an isosceles triangle
00:11 A right angle equals 90
00:14 In an isosceles triangle, the base angles are equal
00:17 These angles are equal and add up to 180, therefore they equal 45
00:20 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the isosceles right-angled triangle below.

Calculate its angles.

2

Step-by-step solution

Let's remember that the sum of angles in a triangle is equal to 180 degrees.

In a right-angled triangle, there is one right angle equal to 90 degrees.

In an isosceles triangle, the base angles are equal to each other.

Therefore, we can calculate this in the following way:

18090=90 180-90=90

90:2=45 90:2=45

In other words, the angle values in this triangle are 90, 45, and 45.

3

Final Answer

90, 45, 45

Key Points to Remember

Essential concepts to master this topic
  • Rule: Sum of all triangle angles always equals 180 degrees
  • Technique: Subtract the right angle: 18090=90 180 - 90 = 90 , then divide by 2
  • Check: Add all angles together: 90+45+45=180 90 + 45 + 45 = 180

Common Mistakes

Avoid these frequent errors
  • Forgetting that isosceles means two equal angles
    Don't assume all three angles are equal or randomly pick angles = wrong answer like 30-60-90! In isosceles triangles, only the BASE angles are equal, not all three. Always identify which two sides are equal first, then find their opposite angles.

Practice Quiz

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

FAQ

Everything you need to know about this question

Which angles are equal in an isosceles right triangle?

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The two base angles are equal! Since one angle is 90°, the other two must be equal to each other. They're the angles opposite the equal sides.

Why are the base angles 45° each?

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After subtracting the right angle (90°) from 180°, you get 90°. Since the two base angles are equal, divide: 90÷2=45° 90 \div 2 = 45° for each angle.

How do I know which angle is 90°?

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Look for the right angle symbol (small square) in the triangle diagram. This marks the 90° angle. The other two angles are across from the equal sides.

Can I use this method for any isosceles triangle?

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Yes! The process is the same:

  • Identify the different angle (could be acute or obtuse)
  • Subtract it from 180°
  • Divide the result by 2 for the equal angles

What if I get decimal answers?

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That's fine! Not all triangles have nice whole number angles. Just make sure your three angles still add up to exactly 180°.

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