Last one I need help on:
The measure of one angle is 38 degrees less than the measure of its supplement. Find the measure of each angle.
x+y=180
y= x+38
x+(x+38)= 180
2x+38=180
-38 =-38
2x = 142
x= 71
plug it in equation
71+71+38= 180
angle 1 = 71
angle 2 = 109
Well, well, well, it looks like we've got ourselves a puzzler.
Let's call the measure of one angle x. Now, we know that the measure of its supplement is 38 degrees more than that, so we can say the measure of the supplement is x + 38.
Now, since the sum of the measures of an angle and its supplement is always 180 degrees, we can set up the equation:
x + (x + 38) = 180
Simplifying that, we get:
2x + 38 = 180
Subtracting 38 from both sides, we have:
2x = 142
Now, divided both sides by 2:
x = 71
So, one angle is 71 degrees, and its supplement is 71 + 38 = 109 degrees.
There you have it, my friend! One angle measures 71 degrees, and its supplement measures 109 degrees.
To solve this problem, let's start by defining the two angles. Let's call the first angle x.
According to the problem, the measure of the second angle is 38 degrees more than the first angle (which is the supplement of the first angle). So, the measure of the second angle can be expressed as (x + 38).
Now, since the sum of the measures of two supplementary angles is always 180 degrees, we can write the following equation:
x + (x + 38) = 180
Simplifying this equation, we get:
2x + 38 = 180
Subtracting 38 from both sides, we have:
2x = 180 - 38
Simplifying further, we get:
2x = 142
Next, to solve for x, we divide both sides of the equation by 2:
x = 71
Therefore, the first angle measures 71 degrees.
To find the measure of the second angle, we substitute the value of x into the expression we defined earlier:
Second angle = (x + 38) = (71 + 38) = 109
Hence, the second angle measures 109 degrees.
To solve this problem, let's start by defining the angles.
Let's call the measure of one angle x. The supplement of this angle is the angle that, when added to the first angle, gives a total of 180 degrees. So, the measure of the supplement is 180 - x.
According to the problem statement, the measure of one angle is 38 degrees less than the measure of its supplement. This can be written as:
x = (180 - x) - 38
Now, let's solve this equation step by step:
1. Distribute the negative sign on the right side:
x = 180 - x - 38
2. Combine the variables on the right side:
x + x = 180 - 38
2x = 142
3. Divide both sides by 2 to isolate x:
x = 142 / 2
x = 71
So, the measure of one angle is 71 degrees.
To find the measure of its supplement, we can substitute this value back into the equation:
Supplement angle = 180 - x
= 180 - 71
= 109
Therefore, the measure of each angle is 71 degrees and 109 degrees.