Obtuse Triangle Practice Problems & Exercises Online

Master obtuse triangles with interactive practice problems. Learn to identify obtuse angles, calculate missing angles, and solve triangle classification exercises step-by-step.

📚What You'll Master in Obtuse Triangle Practice
  • Identify obtuse triangles by recognizing angles greater than 90 degrees
  • Calculate missing obtuse angles using the 180-degree triangle angle sum
  • Compare angle sizes in obtuse triangles to determine relationships
  • Solve algebraic equations to find unknown obtuse angle measurements
  • Classify triangles as obtuse, acute, or right using the Pythagorean theorem
  • Apply obtuse triangle properties to solve real-world geometry problems

Understanding Obtuse Triangle

Complete explanation with examples

Obtuse Triangle Definition

An obtuse triangle is a triangle that has one obtuse angle (greater than 90° 90° degrees and less than 180° 180° degrees) and two acute angles (each of which is less than 90° 90° degrees). The sum of all three angles together is 180° 180° degrees.

Detailed explanation

Practice Obtuse Triangle

Test your knowledge with 20 quizzes

Is the triangle in the drawing an acute-angled triangle?

Examples with solutions for Obtuse Triangle

Step-by-step solutions included
Exercise #1

What kid of triangle is given in the drawing?

90°90°90°AAABBBCCC

Step-by-Step Solution

The measure of angle C is 90°, therefore it is a right angle.

If one of the angles of the triangle is right, it is a right triangle.

Answer:

Right triangle

Video Solution
Exercise #2

What kind of triangle is given in the drawing?

404040707070707070AAABBBCCC

Step-by-Step Solution

As all the angles of a triangle are less than 90° and the sum of the angles of a triangle equals 180°:

70+70+40=180 70+70+40=180

The triangle is isosceles.

Answer:

Isosceles triangle

Video Solution
Exercise #3

What kid of triangle is the following

393939107107107343434AAABBBCCC

Step-by-Step Solution

Given that in an obtuse triangle it is enough for one of the angles to be greater than 90°, and in the given triangle we have an angle C greater than 90°,

C=107 C=107

Furthermore, the sum of the angles of the given triangle is 180 degrees so it is indeed a triangle:

107+34+39=180 107+34+39=180

The triangle is obtuse.

Answer:

Obtuse Triangle

Video Solution
Exercise #4

What kind of triangle is given in the drawing?

999555999AAABBBCCC

Step-by-Step Solution

Given that sides AB and AC are both equal to 9, which means that the legs of the triangle are equal and the base BC is equal to 5,

Therefore, the triangle is isosceles.

Answer:

Isosceles triangle

Video Solution
Exercise #5

Which kind of triangle is given in the drawing?

666666666AAABBBCCC

Step-by-Step Solution

As we know that sides AB, BC, and CA are all equal to 6,

All are equal to each other and, therefore, the triangle is equilateral.

Answer:

Equilateral triangle

Video Solution

Frequently Asked Questions

What makes a triangle obtuse?

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An obtuse triangle has one angle greater than 90° but less than 180°, and two acute angles less than 90°. The sum of all three angles always equals 180°, just like any triangle.

How do you find the obtuse angle in a triangle?

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To find an obtuse angle: 1) Add the two known acute angles, 2) Subtract their sum from 180°, 3) The result is your obtuse angle. Remember, the obtuse angle is always the largest angle in the triangle.

Can a triangle have two obtuse angles?

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No, a triangle cannot have two obtuse angles. Since each obtuse angle is greater than 90°, two obtuse angles would sum to more than 180°, which exceeds the total angle sum possible in any triangle.

What's the difference between obtuse and acute triangles?

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Obtuse triangles have one angle greater than 90°, while acute triangles have all three angles less than 90°. Obtuse triangles appear "wider" or more "spread out" compared to the sharper appearance of acute triangles.

How do you use the Pythagorean theorem to identify obtuse triangles?

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For sides a, b, and c (where c is longest): If a² + b² < c², the triangle is obtuse. If a² + b² = c², it's right. If a² + b² > c², it's acute.

What are common mistakes when solving obtuse triangle problems?

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Common errors include: forgetting that only ONE angle can be obtuse, miscalculating the 180° angle sum, confusing obtuse angles (>90°) with reflex angles (>180°), and incorrectly applying the Pythagorean theorem for classification.

Are obtuse triangles used in real life?

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Yes! Obtuse triangles appear in architecture (roof designs), engineering (bridge supports), art (geometric patterns), and navigation (triangulation methods). Understanding their properties helps in construction and design fields.

What formulas do I need for obtuse triangle practice problems?

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Key formulas include: Angle sum (A + B + C = 180°), Pythagorean test (a² + b² vs c²), and basic algebraic manipulation for solving angle relationships like A = 2B or C = ½A.

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