Question

According to the triangle sum theorem, what is the relationship between the angles in the triangle with angles 15x, 40°, and 80°?

a) The angles are all equal.
b) The sum of the angles is 135x + 120°.
c) The sum of the angles is 135x + 120° - 180°.
d) The angles cannot be determined from the information given.

Answer 1

The relationship between the angles in a triangle with angles 15x, 40°, and 80° can be determined using the Triangle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees. Solving the equation, we find that the angle with 15x is equal to 60 degrees, the angle with 40 degrees remains the same, and the angle with 80 degrees remains the same.

Step-by-step explanation:

The relationship between the angles in a triangle can be determined using the Triangle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees.

Given the angles 15x, 40°, and 80°, we can set up the equation:

15x + 40 + 80 = 180

Combining like terms, we have:

15x + 120 = 180

Subtracting 120 from both sides, we get:

15x = 60

Dividing both sides by 15, we find:

x = 4

Therefore, the relationship between the angles in the triangle is that the angle with 15x is equal to 60 degrees, the angle with 40 degrees remains the same, and the angle with 80 degrees remains the same.