Finding All Angles in an Isosceles Triangle with 62° Base Angle

Isosceles Triangle Properties with Base Angles

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

626262AAABBBCCC

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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 Substitute in the angle value according to the given data
00:11 Determine the sum of the known angles
00:15 The sum of the angles in a triangle equals 180
00:18 Subtract the known angles from this sum in order to find the angle
00:26 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 using the data in the figure.

626262AAABBBCCC

2

Step-by-step solution

In an isosceles triangle, the base angles are equal to each other—that is, angles C and B are equal.

C=B=62 C=B=62

Now we can calculate the vertex angle.

Remember that the sum of angles in a triangle is equal to 180 degrees, therefore:

A=1806262=56 A=180-62-62=56

The values of the angles in the triangle are 62, 62, and 56.

3

Final Answer

62, 62, 56

Key Points to Remember

Essential concepts to master this topic
  • Isosceles Rule: Base angles are always equal in isosceles triangles
  • Calculation: Find vertex angle using A=180°62°62°=56° A = 180° - 62° - 62° = 56°
  • Check: All three angles must sum to exactly 180°: 62 + 62 + 56 = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Assuming all angles are equal instead of just base angles
    Don't think all three angles equal 62° = 186° total! This violates the triangle angle sum rule. Always remember that only the two base angles are equal in an isosceles triangle.

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 the diagram, angles B and C are at the base of the triangle, so they're equal to 62°.

What if I'm given the vertex angle instead of a base angle?

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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: if vertex = 40°, then each base angle = 180°40°2=70° \frac{180° - 40°}{2} = 70°

Can an isosceles triangle have two different base angles?

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No! By definition, an isosceles triangle has exactly two equal sides, which means the angles opposite those sides (base angles) must be equal too.

Why does the angle sum always equal 180°?

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This is a fundamental property of all triangles! No matter what type of triangle you have, the three interior angles will always add up to exactly 180°.

What's special about the vertex angle in an isosceles triangle?

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The vertex angle is the angle between the two equal sides. It's usually different from the base angles and determines the triangle's exact shape.

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