Triangles (Sum of Interior Angles) by Wrestle with Math

Summary

In this video, Dr. Nelson explains the concept of the interior angles of a triangle, emphasizing that the sum of the three interior angles always equals 180°. The video walks through various examples and equations to help viewers understand how to solve for unknown angles in triangles. Using simple algebraic steps, viewers learn to apply the rule of 180° to find missing angle measures. The video includes both basic and more complex problems, with practice opportunities for viewers to try on their own, reinforcing the concept and providing solutions.

Takeaways

• 😀 The sum of the interior angles of any triangle always equals 180°.
• 😀 The rule applies to all types of triangles: right, scalene, equilateral, etc.
• 😀 To solve for unknown angles in a triangle, set up an equation where the sum of the angles equals 180°.
• 😀 The equation for solving unknown angles is: Angle 1 + Angle 2 + Angle 3 = 180°.
• 😀 To simplify, combine like terms and isolate the unknown variable to solve for it.
• 😀 For example, if given x + 75 + 50 = 180, solve by subtracting 125 from both sides to find x = 55°.
• 😀 If the triangle includes a right angle (90°), use that value in the equation.
• 😀 Always check your work by adding the found angles and ensuring they sum to 180°.
• 😀 In a more complex problem, such as x + 37 + x + 67 + 90 = 180, combine like terms before solving for x.
• 😀 For practice, you can solve problems like finding the third angle of a triangle when the first two angles are known.
• 😀 The practice problem examples demonstrate how to apply the rule and check the solution by adding up the angles to confirm the sum is 180°.

Q & A

What is the key rule regarding the interior angles of a triangle?

The sum of the interior angles of any triangle always adds up to 180°.

Does the rule about the sum of the interior angles apply to all types of triangles?

Yes, the sum of the interior angles of a triangle is always 180° regardless of whether it is an equilateral, isosceles, scalene, or right triangle.

How can we solve for an unknown angle in a triangle using this rule?

You can create an equation where the sum of the three angles equals 180°, and then solve for the unknown angle algebraically.

In the first example, how do you solve for the missing angle?

The equation is x + 75 + 50 = 180. Simplifying this gives x + 125 = 180, and solving for x gives x = 55°.

What is the difference in the second example when solving for the missing angle?

The second example involves a right triangle, where one angle is already 90°. The equation becomes 2x + 194 = 180, and solving for x gives x = 7°.

Why do we subtract 194 from both sides in the second example?

We subtract 194 from both sides to isolate the term with the variable (2x) and solve for the unknown value of x.

In the second example, why does x equal 7?

By solving the equation 2x = -14, we find x = -7. This value is then used to find the angle measures.

How do we verify the correctness of the angles in the second example?

We substitute x = -7 into the angle expressions, and check if the sum of the three angles equals 180°. The result confirms that the angles are correct.

What happens when you add the angles in the first practice problem?

In the first practice problem, the angles are 20°, 130°, and the missing angle. The sum of 20° and 130° is 150°, so the missing angle must be 30° to add up to 180°.

How does the second practice problem relate to the examples in the video?

The second practice problem is very similar to the earlier example in the video, involving the equation 2x + 194 = 180, and results in the same solution, x = -7.