Identify the Triangle Type: Analysis of 60° Angle Properties

Triangle Classification with Angle Sum Properties

Identify which type of triangle appears in the drawing:

606060

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine what type of triangle is shown in the drawing
00:03 The sum of the angles in a triangle equals 180
00:06 Apply this equation and proceed to solve for A
00:15 Isolate A
00:31 This is the value of A
00:34 Substitute in this value and determine the triangle's angles
00:38 Based on the angles, the triangle is acute
00:42 This is the solution

Step-by-step written solution

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1

Understand the problem

Identify which type of triangle appears in the drawing:

606060

2

Step-by-step solution

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

Let's calculate alpha in the following way:

60+α+α2=180 60+\alpha+\frac{\alpha}{2}=180

60+112α=180 60+1\frac{1}{2}\alpha=180

112α=18060 1\frac{1}{2}\alpha=180-60

112α=120 1\frac{1}{2}\alpha=120

Let's divide both sides by 1.5:

α=80 \alpha=80

Now we can calculate the remaining angle in the triangle:

α2=802=40 \frac{\alpha}{2}=\frac{80}{2}=40

So in the triangle we have 3 angles: 60, 80, 40

All of them are less than 90 degrees, therefore all angles are acute angles and the triangle is an acute triangle.

3

Final Answer

Acute triangle

Key Points to Remember

Essential concepts to master this topic
  • Rule: All angles in any triangle must sum to exactly 180°
  • Technique: Set up equation: 60° + α + α/2 = 180°, solve for α = 80°
  • Check: Verify all angles are less than 90°: 60°, 80°, 40° ✓

Common Mistakes

Avoid these frequent errors
  • Assuming triangle type from just one angle
    Don't classify the triangle as acute just because you see 60° = acute angle! One acute angle doesn't guarantee all angles are acute. Always find ALL three angles first, then check if each is less than 90° for acute classification.

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 what α/2 means in the diagram?

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The notation α2 \frac{\alpha}{2} means one angle is half the size of another angle. In this triangle, one angle equals α and another equals α divided by 2.

Why can't I just guess the triangle type from the 60° angle?

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A single angle doesn't determine triangle type! You need all three angles. Even though 60° is acute, the other angles could be obtuse (>90°) or right (=90°).

What's the difference between acute, right, and obtuse triangles?

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Acute: All angles < 90°
Right: One angle = 90°
Obtuse: One angle > 90°
Remember: only one classification applies to each triangle!

How do I solve 60 + 1½α = 180?

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First subtract 60 from both sides: 112α=120 1\frac{1}{2}\alpha = 120
Then divide by 1.5 (or multiply by 23 \frac{2}{3} ): α=80° \alpha = 80°

Can a triangle have two obtuse angles?

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No! If two angles were each greater than 90°, their sum would exceed 180° - but that's already the total for all three angles combined. Only one obtuse angle is possible per triangle.

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