Question

42° less than 6 times the measure of an angle is equal to

12° more than 4 times the measure of the angle.
What is the measure of the angle?

Answer 1

The measure of the angle is 18 degrees.

Step-by-step explanation:

Let's denote the measure of the angle as
`\( x \)` . According to the given information, 42 less than 6 times the measure of the angle is equal to 12 more than 4 times the measure of the angle. Mathematically, this translates to the equation:

`\[6x - 42 = 4x + 12.\]`

To solve for
`\( x \)`, first, we'll simplify the equation by gathering like terms:

`\[6x - 4x = 12 + 42,\]`

`\[2x = 54.\]`

Now, isolate
`\( x \)` by dividing both sides by 2:

`\[x = (54)/(2),\]`

`\[x = 27.\]`

However, this is the value of
`\( x \)` before considering the 42 less than 6 times the measure of the angle. Therefore, to find the actual measure of the angle, we subtract 42 from the calculated value:

`\[x = 27 - 42,\]`

`\[x = 18.\]`

Hence, the measure of the angle is 18 degrees.