In a triangle, the measure of the first angle is four times the measure of the second angle. The measure of the third angle is 84 degrees more than the second angle. what is the measure of the first angle?

second angle --- x

first angle ------ 4x
third angle ----- x+84

x + 4x + x+84 = 180

you finish it

Thanks for your help Reiny.

To find the measure of the first angle, we need to follow a few steps.

Step 1: Assign variables:
Let's assign variables to the angles:
- Let's call the second angle "x".
- Since the first angle is four times the measure of the second angle, we can represent it as "4x".
- The measure of the third angle is 84 degrees more than the second angle, so we can represent it as "x + 84".

Step 2: Set up an equation:
In a triangle, the sum of the angles is always 180 degrees. So, we can write the equation:
(first angle) + (second angle) + (third angle) = 180

Substituting our assigned variables into the equation, we get:
4x + x + (x + 84) = 180

Step 3: Solve the equation:
Combine like terms:
6x + 84 = 180

Subtract 84 from both sides of the equation:
6x = 96

Divide both sides by 6:
x = 16

Step 4: Find the measure of the first angle:
Substitute the value of x back into the equation for the first angle:
4x = 4 * 16 = 64

Therefore, the measure of the first angle is 64 degrees.