Solve for X: Finding Angles 4x and 2x in an Isosceles Triangle

Isosceles Triangle with Angle Variables

ABC is an isosceles triangle.

A=4x ∢A=4x

B=2x ∢B=2x

Calculate the value of x.

AAABBBCCC4x2x

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate X
00:03 isosceles triangle according to the given data
00:07 in an isosceles triangle, the base angles are equal
00:18 the sum of angles in a triangle equals 180
00:26 let's collect terms and isolate X
00:46 and this is the solution to the question

Step-by-step written solution

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1

Understand the problem

ABC is an isosceles triangle.

A=4x ∢A=4x

B=2x ∢B=2x

Calculate the value of x.

AAABBBCCC4x2x

2

Step-by-step solution

As we know that triangle ABC is isosceles.

B=C=2X B=C=2X

It is known that in a triangle the sum of the angles is 180.

Therefore, we can calculate in the following way:

2X+2X+4X=180 2X+2X+4X=180

4X+4X=180 4X+4X=180

8X=180 8X=180

We divide the two sections by 8:

8X8=1808 \frac{8X}{8}=\frac{180}{8}

X=22.5 X=22.5

3

Final Answer

22.5

Key Points to Remember

Essential concepts to master this topic
  • Triangle Rule: Sum of all angles equals 180 degrees
  • Technique: Identify equal angles: B=C=2x ∢B = ∢C = 2x
  • Check: Verify angles: 45° + 45° + 90° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting which angles are equal in isosceles triangles
    Don't assume angle A has equal sides and equal angles = wrong setup! In isosceles triangles, the angles opposite the equal sides are equal. Always identify the base angles first, then use the fact that they're equal.

Practice Quiz

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Indicates which angle is greater

FAQ

Everything you need to know about this question

How do I know which angles are equal in an isosceles triangle?

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In an isosceles triangle, the base angles (angles opposite the equal sides) are always equal. Look at the diagram - if sides AB and AC are equal, then B=C ∢B = ∢C .

Why is angle B equal to angle C in this problem?

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Since triangle ABC is isosceles and we're given B=2x ∢B = 2x , the other base angle C ∢C must also equal 2x 2x . This is the key property of isosceles triangles!

What if I set up the equation wrong?

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Always write down what you know first: A=4x ∢A = 4x , B=C=2x ∢B = ∢C = 2x . Then use the fact that all angles sum to 180°. This systematic approach prevents setup errors.

How can I check if x = 22.5 is correct?

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Substitute back: A=4(22.5)=90° ∢A = 4(22.5) = 90° , B=C=2(22.5)=45° ∢B = ∢C = 2(22.5) = 45° . Check: 90° + 45° + 45° = 180°

Is this triangle a special type?

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Yes! With angles of 45°, 45°, and 90°, this is a 45-45-90 right triangle - a very special isosceles right triangle you'll see often in geometry.

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