Calculate All Angles in an Isosceles Triangle with 50° Angle

Triangle Angle Calculation with Isosceles Properties

Find all the angles of the isosceles triangle using the data in the figure.

505050AAACCCBBB

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Step-by-step video solution

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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)
00:15 This is the solution

Step-by-step written solution

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1

Understand the problem

Find all the angles of the isosceles triangle using the data in the figure.

505050AAACCCBBB

2

Step-by-step solution

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

B=C B=C

Since we are given angle A, we can calculate the base angles as follows:

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

18050=130 180-50=130

130:2=65 130:2=65

B=C=65 B=C=65

3

Final Answer

B=65,C=65 B=65,C=65

Key Points to Remember

Essential concepts to master this topic
  • Isosceles Rule: Base angles are always equal to each other
  • Technique: Subtract vertex angle from 180°: 180°50°=130° 180° - 50° = 130°
  • Check: Verify all angles sum to 180°: 50°+65°+65°=180° 50° + 65° + 65° = 180°

Common Mistakes

Avoid these frequent errors
  • Assuming the given angle is a base angle
    Don't assume 50° is a base angle and make the other base angle different = wrong triangle type! This creates a scalene triangle instead of isosceles. Always identify which angle is the vertex angle first, then use the fact that base angles are equal.

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 angle is the vertex angle?

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Look at the diagram carefully! The vertex angle is at the top of the triangle between the two equal sides. In this problem, angle A (50°) is clearly at the vertex position.

What if the given angle was at the base instead?

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If 50° was a base angle, then both base angles would be 50°. The vertex angle would be: 180°50°50°=80° 180° - 50° - 50° = 80° . Always check the diagram to see the angle's position!

Can an isosceles triangle have a 90° angle?

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Yes! An isosceles right triangle has a 90° vertex angle and two 45° base angles. It's still isosceles because two sides are equal.

Why do we divide 130° by 2?

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Because the two base angles are equal and they must share the remaining degrees equally. Since 180°50°=130° 180° - 50° = 130° , each base angle gets 130°÷2=65° 130° ÷ 2 = 65° .

What's the difference between isosceles and equilateral triangles?

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Isosceles: Two equal sides and two equal angles
Equilateral: All three sides equal and all angles are 60°
Every equilateral triangle is also isosceles, but not every isosceles triangle is equilateral!

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