Find All Angles in an Isosceles Triangle with 50° Base Angle

Isosceles Triangle Properties with Given Base Angle

Calculate the remaining angles in the isosceles triangle below.

505050AAACCCBBB

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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 In an isosceles triangle (given) the base angles are equal
00:07 Insert the angle value according to the given data
00:11 Determine the sum of the known angles
00:16 The sum of angles in a triangle equals 180
00:20 Subtract the known angles from this sum in order to find the angle:
00:24 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Calculate the remaining angles in the isosceles triangle below.

505050AAACCCBBB

2

Step-by-step solution

Since we know that the triangle is isosceles, we know that the base angles are equal.

That is:

B=C=50 B=C=50

Now we can calculate the vertex angle.

Since the sum of angles in a triangle is equal to 180 degrees, we will calculate the vertex angle as follows:

A=1805050=80 A=180-50-50=80

Therefore, the values of the angles are 80, 50, and 50.

3

Final Answer

A=80,C=50 A=80,C=50

Key Points to Remember

Essential concepts to master this topic
  • Base Angles: In isosceles triangles, the two base angles are always equal
  • Calculation: If base angle = 50°, then vertex angle = 180° - 50° - 50° = 80°
  • Verification: Check that all three angles sum to exactly 180° ✓

Common Mistakes

Avoid these frequent errors
  • Assuming the given angle is the vertex angle
    Don't assume the 50° angle is at the top vertex = you'll calculate 65° for each base angle! The diagram shows 50° is a base angle at the bottom. Always identify which angle type is given first.

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 bottom (the base), so they're equal. The vertex angle A is at the top where the two equal sides meet.

What if I'm told the vertex angle instead?

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If you know the vertex angle, subtract it from 180°, then divide by 2 to find each base angle. For example: vertex = 80°, so each base angle = (180° - 80°) ÷ 2 = 50°.

Can an isosceles triangle have a 90° angle?

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Yes! If the vertex angle is 90°, then each base angle would be 45°. This creates a right isosceles triangle, which is very common in geometry problems.

Why are the base angles always equal?

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In an isosceles triangle, the two sides of equal length create identical conditions at their endpoints. This symmetry forces the angles opposite these equal sides to be equal too.

How can I remember which angles are equal?

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  • Equal sides → Equal opposite angles
  • The base angles are always the ones not between the equal sides
  • Think: "same sides, same angles"

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