Isosceles Triangle: Finding Angle X When Base Angle is 55 Degrees

Q: How do I know which angles are the base angles?

The base angles are opposite the two equal sides! Since AB = AC, angles B and C are the base angles. The vertex angle is at A, between the two equal sides.

Q: Why can't all three angles be 55°?

If all angles were 55°, the sum would be 165°, not 180°! Triangle angles must always add up to exactly 180°.

Q: Can I solve this without knowing it's isosceles?

No! The fact that it's isosceles is crucial because it tells you that two angles are equal. Without this information, you can't find the specific angle values.

Triangle Properties with Base Angle Calculations

ABC is an isosceles triangle.

AB = AC

Angle B equals 55 degrees.

Find the value X.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:06 An isosceles triangle according to the given data

00:09 Base angles are equal in an isosceles triangle

00:19 The sum of angles in a triangle equals 180

00:25 Therefore it is the complementary angle to 180

00:35 Let's substitute appropriate values according to the given data and solve for the angle

00:41 This is angle BAC

00:48 Vertical angles are equal

00:51 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

ABC is an isosceles triangle.

AB = AC

Angle B equals 55 degrees.

Find the value X.

Step-by-step solution

Since this is an isosceles triangle, angle B and angle C are equal to each other.

$B=C=55$

Therefore we can calculate angle A since the sum of the angles in the triangle equals 180:

$A=180-55-55=180-110=70$

Since angle X is the vertex of angle A, they are equal, hence:

$A=X=70$

Final Answer

$70$

Key Points to Remember

Essential concepts to master this topic

Rule: In isosceles triangles, base angles are always equal
Technique: Use angle sum property: 180° - 55° - 55° = 70°
Check: Verify all angles sum to 180°: 70° + 55° + 55° = 180° ✓

Common Mistakes

Avoid these frequent errors

Assuming all angles in isosceles triangle are equal
Don't think isosceles means all angles are 60° like equilateral triangles = wrong vertex angle! Only the BASE angles are equal in isosceles triangles. Always identify which two sides are equal to find the correct base angles.

Practice Quiz

Test your knowledge with interactive questions

If one of two corresponding angles is a right angle, then the other angle will also be a right angle.

FAQ

Everything you need to know about this question

How do I know which angles are the base angles?

The base angles are opposite the two equal sides! Since AB = AC, angles B and C are the base angles. The vertex angle is at A, between the two equal sides.

Why can't all three angles be 55°?

If all angles were 55°, the sum would be 165°, not 180°! Triangle angles must always add up to exactly 180°.

What if the problem gave me angle C instead of angle B?

It wouldn't matter! Since this is an isosceles triangle with AB = AC, angles B and C are always equal. So angle C would also be 55°.

Is X always the vertex angle?

Look at the diagram carefully! X is marked at vertex A, which is where the two equal sides meet. This makes X the vertex angle, not a base angle.

Can I solve this without knowing it's isosceles?

No! The fact that it's isosceles is crucial because it tells you that two angles are equal. Without this information, you can't find the specific angle values.

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