Determine Triangle Type Using Angles X, 3X, and 5X

Triangle Classification with Angle Variables

Identify which type of triangle appears in the drawing:

XXX3X3X3X5X5X5X

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 First, let's find out what type of triangle we have in the drawing.
00:08 Remember, the angles in a triangle add up to 180 degrees.
00:13 Let's use this fact to find the value of X. Ready?
00:17 Great! Now, let's solve for X. Isolate the variable X.
00:22 Well done! We have our value for X.
00:26 Next, substitute this value into our angle equations to find the triangle's angles.
00:36 Look! With these angles, we can see the triangle is obtuse.
00:41 And that's our solution! Nice work!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Identify which type of triangle appears in the drawing:

XXX3X3X3X5X5X5X

2

Step-by-step solution

Note that the sum of angles in a triangle equals 180 degrees.

Let's calculate X in the following way:

3x+5x+x=180 3x+5x+x=180

9x=180 9x=180

Let's divide both sides by 9:

x=20 x=20

Now let's calculate the angles:

3x=3×20=60 3x=3\times20=60

5x=5×20=100 5x=5\times20=100

This means that in the triangle we have 3 angles: 20, 60, 100

Given that we have one angle that is greater than 90 degrees, meaning an obtuse angle, this is an obtuse triangle.

3

Final Answer

Obtuse triangle

Key Points to Remember

Essential concepts to master this topic
  • Rule: Sum of triangle angles equals 180 degrees always
  • Technique: Set up equation x + 3x + 5x = 180, solve to get x = 20
  • Check: Verify angles are 20°, 60°, 100° and sum equals 180° ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to find actual angle measures after solving for x
    Don't stop at x = 20 without calculating the actual angles! This leaves you unable to classify the triangle type. Always substitute x back into each expression: x = 20°, 3x = 60°, 5x = 100° to determine if any angle exceeds 90°.

Practice Quiz

Test your knowledge with interactive questions

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 if a triangle is obtuse just from the angles?

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A triangle is obtuse if any one angle is greater than 90°. In this problem, since 5x = 100° > 90°, it's an obtuse triangle. Only one angle needs to be obtuse!

Why can't I just look at the variables x, 3x, 5x to classify the triangle?

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The variables alone don't tell you the actual angle measures! You must solve for x first, then calculate each angle. The same variables could give different triangle types depending on the value of x.

What if I get a negative value for x?

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Check your algebra! Since angles in a triangle are always positive, x must be positive. If you get negative values, you likely made an error in setting up or solving the equation x+3x+5x=180 x + 3x + 5x = 180 .

Can a triangle have two obtuse angles?

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No, impossible! If two angles were each greater than 90°, their sum alone would exceed 180°. Since all three angles must sum to exactly 180°, only one angle can be obtuse.

How do I remember the difference between acute, right, and obtuse triangles?

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  • Acute: All angles < 90°
  • Right: Exactly one angle = 90°
  • Obtuse: Exactly one angle > 90°

Just check the largest angle to classify the triangle!

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