a. Write an equation that would help you solve for the missing angle measures. Combine Like Terms! Remember the Triangle Sum Theorem. b. Solve the equation to find the value of x. Show/Explain all of your steps using inverse operations!
a. The Triangle Sum Theorem states that the sum of the interior angles in a triangle is equal to 180 degrees.
Let's assume that the three angles in the triangle are A, B, and C.
The equation that represents the sum of the angles in the triangle is:
A + B + C = 180 degrees
b. Let's say the value of x represents one angle in the triangle.
Using the equation from part a, we can write:
x + (2x + 10) + (3x - 10) = 180
Combine like terms:
x + 2x + 3x + 10 - 10 = 180
6x = 180
Now, we can solve for x by dividing both sides of the equation by 6:
(6x)/6 = 180/6
x = 30
So, the value of x is 30.
can you redo this info but with different numbers
Certainly! Here's an alternative example:
a. Let's assume the angles in the triangle are A, B, and C.
The equation representing the sum of the angles in the triangle is:
A + B + C = 180 degrees
b. Let's say the value of x represents one angle in the triangle.
Using the equation from part a, we can write:
x + (3x + 20) + (2x - 10) = 180
Combine like terms:
x + 3x + 2x + 20 - 10 = 180
6x + 10 = 180
Now, let's isolate the variable by subtracting 10 from both sides of the equation:
6x + 10 - 10 = 180 - 10
6x = 170
Next, divide both sides of the equation by 6 to solve for x:
(6x)/6 = 170/6
x = 28.33
So, the value of x is approximately 28.33.