Question

The measures of the three angles of a triangle are given by 4x-1, 2x+1, and 6x. What is the measure of the largest angle?

Answer 1

The largest angle in the triangle measures 90 degrees after solving the equation formed by the sum of the triangle's angles, which must equal 180 degrees.

Step-by-step explanation:

To determine the measure of the largest angle in the triangle with angles given as 4x-1, 2x+1, and 6x, we use the fact that the sum of the angles in a triangle equals 180 degrees.

First, add all three angles to set up the equation: (4x-1) + (2x+1) + 6x = 180.

Next, simplify the equation: 12x = 180.

Then, solve for x: x = 180 / 12 = 15.

Now that we know the value of x, we can find the angles:

Angle 1: 4x-1 = 4(15)-1 = 59 degrees

Angle 2: 2x+1 = 2(15)+1 = 31 degrees

Angle 3: 6x = 6(15) = 90 degrees

Thus, the measure of the largest angle is 90 degrees.