2 angles are supplementary if their sum is 180degress. Larger angle measures four degrees more than seven times the smaller angle. X represent the smaller angle and these two angles are supplementary. Find measure of each angle.
The larger angle would be 4 + 7x and the smaller would be x. They both add up to 180, so (x) + (7x + 4) = 180. This is 8x + 4 = 180. 8x = 176. x = 22. The smaller angle is 22.
The larger angle is 7x + 4, 7(22) + 4, 154 + 4 = 158
The 2 angles are 158 and 22.
Well, well! Looks like we've got a little math problem to solve. Let's dive in, shall we?
We know that the sum of two supplementary angles is 180 degrees. So, we can write down our first equation:
x + (7x + 4) = 180
Now, let's simplify this equation:
8x + 4 = 180
To solve for x, we need to get rid of that pesky little 4. We can do that by subtracting 4 from both sides:
8x = 176
You're doing great! Now we just need to solve for x. We divide both sides by 8:
x = 22
Fantastic! We've now found the value of x, which represents the smaller angle. Now, to find the larger angle, we can substitute x back into our equation:
7x + 4 = 7(22) + 4 = 158 + 4 = 162
So, the smaller angle measures 22 degrees, and the larger angle measures 162 degrees. Ta-da! Problem, solved!
Let's represent the smaller angle as 'x' and the larger angle as '7x + 4'. Since the sum of these two angles is 180 degrees due to being supplementary, we can set up the equation:
x + 7x + 4 = 180
Combining like terms, we get:
8x + 4 = 180
Now, let's isolate 'x' by subtracting 4 from both sides:
8x = 176
To solve for 'x', divide both sides by 8:
x = 22
So, the smaller angle 'x' measures 22 degrees.
To find the larger angle, substitute the value of 'x' back into the equation:
7x + 4 = 7 * 22 + 4 = 154 + 4 = 158
Therefore, the larger angle measures 158 degrees.
To solve this problem, we need to set up an equation based on the given information and then solve for the variables.
Let's assume that the smaller angle is represented by x degrees.
According to the given information, the larger angle measures four degrees more than seven times the smaller angle. Therefore, the larger angle can be represented as 7x + 4 degrees.
Since the two angles are supplementary, their sum is 180 degrees. We can set up the equation:
x + (7x + 4) = 180
Now, let's solve this equation to find the value of x:
Combine like terms:
8x + 4 = 180
Subtract 4 from both sides:
8x = 176
Divide both sides by 8:
x = 22
So, the smaller angle measures 22 degrees.
Now, to find the measure of the larger angle, we substitute x = 22 into the equation for the larger angle:
7x + 4 = 7(22) + 4 = 154 + 4 = 158
Therefore, the larger angle measures 158 degrees.
To recap:
- The smaller angle measures 22 degrees.
- The larger angle measures 158 degrees.