Calculate All Angles in an Isosceles Triangle with 70° Vertex Angle

Triangle Angle Sum with Equal Base Angles

Find all the angles of the isosceles triangle below:

707070AAABBBCCC

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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
00:06 Subtract the known angle from this sum
00:09 This is the sum of the remaining angles
00:12 Divide by 2 given that they are equal (isosceles triangle)
00:16 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Find all the angles of the isosceles triangle below:

707070AAABBBCCC

2

Step-by-step solution

Let's remember that in an isosceles triangle, the base angles are equal to each other.

In other words:

C=B C=B

We know the vertex angle, which is equal to 70 degrees, and we know that the sum of angles in a triangle is equal to 180 degrees.

Therefore, we can calculate the base angles in the following way:

18070=110 180-70=110

110:2=55 110:2=55

Therefore, the angle values in the triangle are 55, 55, and 70.

3

Final Answer

70, 55, 55

Key Points to Remember

Essential concepts to master this topic
  • Isosceles Property: Base angles are always equal in isosceles triangles
  • Technique: Subtract vertex angle from 180°, then divide by 2: (180°70°)÷2=55° (180° - 70°) ÷ 2 = 55°
  • Check: All angles sum to 180°: 70° + 55° + 55° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Dividing 70° by 2 to find base angles
    Don't divide the vertex angle by 2 = 35° base angles! This ignores that angles must sum to 180°. Always subtract the vertex angle from 180° first, then divide the remainder by 2.

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

How do I know which angles are the base angles?

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The base angles are the two angles opposite the equal sides. In this triangle, angles B and C are at the base, while angle A (70°) is the vertex angle at the top.

Why are the base angles always equal?

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In an isosceles triangle, the two equal sides create identical triangular shapes on each side. This symmetry means the base angles must be exactly the same size!

What if I got 110° for each base angle?

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That's the total for both base angles combined! Remember to divide by 2: 110°÷2=55° 110° ÷ 2 = 55° for each base angle.

Can I use this method for any isosceles triangle?

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Yes! This method works whenever you know the vertex angle: subtract it from 180°, then divide by 2. The base angles are always equal in isosceles triangles.

How do I check my answer is correct?

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Add all three angles together: they must equal 180°. Also verify that the two base angles are equal to each other: 55° = 55° ✓

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