Question

A triangle has one angle measuring 3x degrees. A second angle measures (2x + 20) degrees, and the third angle measures (4x – 20) degrees. What is the value of x?

A) x = 20
B) x = 30
C) x = 40
D) x = 50

Answer 1

To find x in the given triangle, we set up an equation 3x + (2x + 20) + (4x – 20) = 180 based on the triangle angle sum theorem. Simplifying gives us x = 20, thus the correct answer is A) x = 20.

Step-by-step explanation:

To find the value of x in a triangle with one angle measuring 3x degrees, a second angle measuring (2x + 20) degrees, and a third angle measuring (4x – 20) degrees, we use the fact that the sum of the angles in a triangle is 180 degrees.

We set up an equation based on this fact:

3x + (2x + 20) + (4x – 20) = 180

Combining like terms, we get:

3x + 2x + 4x + 20 - 20 = 180

9x = 180

Now dividing both sides by 9 gives us:

x = 180 / 9

x = 20

So, the correct answer is A) x = 20.