<3 and <4 form a linear pair. The measure of <3 is four more than three times the measure of <4. Find the measure of each angle.

first we represent the unknowns using variables:

let x = measure of angle 4
let 3x+4 = measure of angle 3 (from the second statement)
then we set-up the equation. since the angles form a linear pair, their sum is equal to 180 degrees. therefore,
x + 3x + 4 = 180
4x + 4 = 180
4x = 176
x = 44 degrees (measure of angle 4)
3x + 4 = 136 degrees (measure of angle 3)

hope this helps~ :)

To find the measure of each angle, let's break down the information given.

Given:
1. <3 and <4 form a linear pair.

2. The measure of <3 is four more than three times the measure of <4.

Let's assign variables for the measures of angles <3 and <4. We'll use x for the measure of <4.

Let's solve for the measure of <3:
According to the given information, the measure of <3 is four more than three times the measure of <4, so we can write it as:

Measure of <3 = 3 * Measure of <4 + 4

Now, since <3 and <4 form a linear pair, their sum is 180 degrees. Therefore, we can write the equation:

Measure of <3 + Measure of <4 = 180

Substituting the value of <3 from the first equation, we get:

(3 * Measure of <4 + 4) + Measure of <4 = 180

Simplifying the equation, we have:

3 * Measure of <4 + Measure of <4 + 4 = 180

Combining like terms, we get:

4 * Measure of <4 + 4 = 180

Subtracting 4 from both sides:

4 * Measure of <4 = 176

Dividing both sides by 4:

Measure of <4 = 176/4 = 44 degrees

Now, to find the measure of <3, we substitute the value of <4 (which is 44 degrees) into the equation:

Measure of <3 = (3 * 44) + 4

Measure of <3 = 132 + 4 = 136 degrees

Therefore, the measure of <3 is 136 degrees, and the measure of <4 is 44 degrees.