Angle 3 and angle 4 form a linear pair. The measure of angle 3 is four more than three times the measure of angle 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~ :)
these equations are hard looking
If \large \angle1 and \large \angle2 are vertical angles, \large \angle2 and \large \angle3 are complementary angles, and m\large \angle3=47, find m\large \angle1=
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To find the measure of each angle, let's first define our variables:
Let x be the measure of angle 4.
Since angle 3 is four more than three times the measure of angle 4, we can represent the measure of angle 3 as 3x + 4.
According to the given information, angle 3 and angle 4 form a linear pair. By definition, a linear pair is formed when two angles are adjacent and the sum of their measures is 180 degrees.
Therefore, we can write an equation based on the linear pair:
angle 3 + angle 4 = 180
Substituting the measures we found:
(3x + 4) + x = 180
Combining like terms:
4x + 4 = 180
Subtracting 4 from both sides:
4x = 176
Dividing both sides by 4:
x = 44
Now that we have the measure of angle 4:
angle 4 = x = 44 degrees
To find the measure of angle 3, substitute the value of x into the expression we derived earlier:
angle 3 = 3x + 4 = 3(44) + 4 = 132 + 4 = 136 degrees
Therefore, the measure of angle 3 is 136 degrees and the measure of angle 4 is 44 degrees.