What is the value of ∠c in the diagram? a. 40° b. 60° c. 80° d. 90°

Before we begin, I just want to remind you to not automatically assume that this is an equilateral triangle and that all of its three angles are equivalent, therefore meaning that C = 180 / 3 = 60°. Please DO NOT do this as it is incorrect and especially not possible in this problem as the angles are not equivalent.

If there is no clear indication such as dashes in the diagram or a statement specifying that it is an equilateral triangle, DO NOT assume that it is an equilateral triangle.

Now let's move on to solving the problem.

STEP-BY-STEP SOLUTION:

First let's establish the following formula:

Angle sum of a triangle = 180°

Therefore:

4x + 2x + 3x = 180°

Using the above equation, we will first make ( x ) the subject and solve accordingly as displayed below:

4x + 2x + 3x = 180°

9x = 180

x = 180 / 9

x = 20°

From this, we will substitue the value of x into the equation for C as displayed below:

C = 3x

C = 3 ( 20 )

C = 60°

Therefore, the answer is:

Option B - 60°