∠1 and ∠2 form a linear pair. If m∠1 = 3x - 8 and m∠2 = 5x + 4, find the measure of each angle. The diagram is not to scale.
a linear pair sums to a straight angle. So, you need
3x-8 + 5x+4 = 180
Solve for x, and use that to get the angle measures.
Add like terms:3x+5x=8x,-8+4=-4
you get, 8x-4=180
add 4 to both sides
8x=184
divide
x=23
sub in answers
3*23-8=61
5*23+4=119
add them together
119+61=180
Since ∠1 and ∠2 form a linear pair, their measures add up to 180 degrees. Therefore, we can write the equation as:
m∠1 + m∠2 = 180
Substituting the given values in terms of x:
(3x - 8) + (5x + 4) = 180
Simplifying the equation:
3x + 5x - 8 + 4 = 180
Combining like terms:
8x - 4 = 180
Adding 4 to both sides:
8x = 184
Dividing by 8 on both sides:
x = 23
Now we can substitute the value of x back into the expressions for m∠1 and m∠2:
m∠1 = 3x - 8
m∠2 = 5x + 4
m∠1 = 3(23) - 8
m∠2 = 5(23) + 4
m∠1 = 69 - 8
m∠2 = 115 + 4
m∠1 = 61
m∠2 = 119
Therefore, the measure of ∠1 is 61 degrees and the measure of ∠2 is 119 degrees.
To find the measure of each angle, we start by noting that ∠1 and ∠2 form a linear pair, which means they are adjacent angles and their measures add up to 180 degrees. Let's set up an equation using this information.
The measure of ∠1 is given as m∠1 = 3x - 8.
The measure of ∠2 is given as m∠2 = 5x + 4.
Since the sum of the measures of ∠1 and ∠2 is 180 degrees, we can write the equation:
m∠1 + m∠2 = 180.
Plugging in the given values, we have:
(3x - 8) + (5x + 4) = 180.
Now, we can simplify and solve for x:
8x - 4 = 180.
8x = 180 + 4.
8x = 184.
x = 184/8.
x = 23.
Now that we have the value of x, we can substitute it back into the equations for m∠1 and m∠2 to find their measures:
m∠1 = 3x - 8 = 3(23) - 8 = 69 - 8 = 61 degrees.
m∠2 = 5x + 4 = 5(23) + 4 = 115 + 4 = 119 degrees.
Therefore, the measure of ∠1 is 61 degrees, and the measure of ∠2 is 119 degrees.