the measure of angle 1 is five less than four times the measure of angle 2. if angle 1 and angle 2 form a linear pair, what are their measures?
first, represent unknowns with variables.
let x = measure of angle 2
let 4x-5 = measure of angle 1 (according to the first statement of problem)
then set-up the equation. since the angles form a linear pair, their sum must be equal to 180. thus,
x + 4x - 5 = 180
5x = 180 + 5
5x = 185
x = 37 degrees (measure of angle 2)
4x-5 = 143 degrees (measure of angle 1)
hope this helps~ :)
Well, isn't that acute question! Let's get to the bottom of it.
Let's call the measure of angle 2 "x". According to the given information, we know that angle 1 is five less than four times the measure of angle 2.
So, angle 1 = 4x - 5.
Since angle 1 and angle 2 form a linear pair, the sum of their measures is 180 degrees.
So, angle 1 + angle 2 = 180.
Now we can substitute in the values we found:
4x - 5 + x = 180.
Combining like terms, we get:
5x - 5 = 180.
Adding 5 to both sides:
5x = 185.
Dividing both sides by 5:
x = 37.
Now that we have the value of x, we can find angle 1:
angle 1 = 4(37) - 5.
This gives us:
angle 1 = 143.
So, angle 1 measures 143 degrees and angle 2 measures 37 degrees.
Voila!
Let's assume the measure of angle 2 is x.
According to the problem, the measure of angle 1 is five less than four times the measure of angle 2.
So, angle 1 = 4 * angle 2 - 5 = 4x - 5.
Since angle 1 and angle 2 form a linear pair, they add up to 180 degrees.
Therefore, angle 1 + angle 2 = 180.
Substituting the values, we have:
(4x - 5) + x = 180.
Combining like terms:
5x - 5 = 180.
Adding 5 to both sides:
5x = 185.
Dividing both sides by 5:
x = 37.
So, angle 2 measures 37 degrees.
Substituting this value back into the equation for angle 1:
angle 1 = 4x - 5 = 4(37) - 5 = 148 - 5 = 143.
Therefore, angle 1 measures 143 degrees.
To find the measures of angle 1 and angle 2, we will use the information given.
Let's represent the measure of angle 2 as "x".
According to the question, the measure of angle 1 is five less than four times the measure of angle 2. So, angle 1 can be represented as 4x - 5.
Since angle 1 and angle 2 form a linear pair, their measures add up to 180 degrees.
Therefore, we can set up the equation:
4x - 5 + x = 180
Combining like terms, we get:
5x - 5 = 180
Next, we can isolate the variable by adding 5 to both sides of the equation:
5x - 5 + 5 = 180 + 5
This simplifies to:
5x = 185
Finally, to solve for x, we divide both sides of the equation by 5:
5x/5 = 185/5
x = 37
Now that we have found the value of x, we can substitute it back into our expressions to find the measures of angle 1 and angle 2.
Angle 1 = 4x - 5 = 4(37) - 5 = 148 - 5 = 143 degrees
Angle 2 = x = 37 degrees
Therefore, angle 1 measures 143 degrees and angle 2 measures 37 degrees.