ÂNGULOS NO TRIÂNGULO - SOMA DOS ÂNGULOS INTERNOS DE UM TRIÂNGULO

Summary

In this engaging lesson, Gis walks viewers through solving triangle exercises involving the sum of internal angles. She demonstrates how to find the value of unknown angles by creating equations based on the known sum of triangle angles, which is always 180°. Gis explains step-by-step how to solve for ‘x’ using algebraic methods and provides multiple examples for practice. She also touches on external angles, illustrating how to apply different strategies for solving triangle-related problems. This class is perfect for students looking to strengthen their understanding of geometric angles and improve their math skills.

Takeaways

• 😀 The sum of the internal angles of a triangle always equals 180 degrees.
• 😀 The strategy for solving triangle angle problems involves setting up an equation with the unknown angle(s).
• 😀 The process of solving for the unknown angle(s) includes isolating terms and using basic algebraic techniques.
• 😀 To solve the equation, all terms involving 'x' are grouped on one side, and constant terms are moved to the other side.
• 😀 When solving for 'x', remember to divide by the coefficient of 'x' to isolate its value.
• 😀 Once 'x' is found, substitute it back into the equation to find the values of all the triangle's angles.
• 😀 It's important to check the sum of the angles to ensure that they total 180 degrees as expected.
• 😀 In some problems, the sum of two internal angles will be equal to the external angle (external angle theorem).
• 😀 For triangles with external angles, an alternative method is to add the two internal angles that form the external angle.
• 😀 Always double-check your final answers by ensuring that the sum of the internal angles equals 180 degrees.

Q & A

What is the sum of the internal angles of a triangle?

The sum of the internal angles of a triangle is always 180 degrees.

How do you find the value of the unknown angle in a triangle when given expressions involving variables?

You create an equation by adding the expressions for each angle and setting the sum equal to 180 degrees, since the sum of internal angles in a triangle is always 180 degrees. Then, solve for the variable.

In the example with 'x + 2x + (x + 20)', how is the equation formed?

The equation formed is: x + 2x + (x + 20) = 180. This equation represents the sum of the internal angles of the triangle, where the angles are expressed in terms of x.

What technique does the teacher use to solve the equation in the first example?

The teacher uses the technique of grouping like terms, moving constants to the other side of the equation, and solving for the unknown variable x.

After solving for x, what do you need to do next?

Once you find the value of x, you need to substitute it back into the angle expressions to determine the actual measures of each angle in the triangle.

What are the values of the angles once x is found to be 40 in the first example?

Once x is found to be 40, the angles are: x = 40°, x + 20 = 60°, and 2x = 80°.

How do you check if the calculated angles are correct?

To check if the angles are correct, add them up. If the sum equals 180 degrees, then the angles are correct.

What strategy is used in the second example involving the angles 3x - 15, 3x, and 2x - 5?

The strategy is to form an equation by adding the three angle expressions and equating the sum to 180. Then, solve for x by grouping like terms and isolating the variable.

In the second example, what are the values of the angles after solving for x?

After solving for x (which is 25), the angles are: 3x - 15 = 75°, 3x = 75°, and 2x - 5 = 60°.

What makes the third example different from the previous ones?

The third example is different because it involves an external angle, and the sum of the internal angles adjacent to this external angle is equal to the external angle.