<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.