the sum of four angles about a point is 360degree.the measure of the 2nd angle is 6degreemore than 3times the 1st,the measure of the 3rd is 3degree more than twice the first,the measure of the 4th is 20 degree less than the 3rd.what is the measure of each angle?
Since this is algebra, do you know what algebraic equations you should be writing out and solving for?
math algebra, rhodora, meir ~ Switching names won't get answers for you any faster, as Reiny has already told you.
And when any student wants a "fast answer," it's often assumed he/she is taking a test and just wants the answers.
Please answer Leo's question if you want further help from math tutors. And quit switching names.
To solve this problem, let's assign variables to each angle to help keep track of the information given.
Let's say the measure of the first angle is 'x'.
According to the information given:
- The measure of the second angle is 6 degrees more than 3 times the first angle. This can be represented as 3x + 6.
- The measure of the third angle is 3 degrees more than twice the first angle. This can be represented as 2x + 3.
- The measure of the fourth angle is 20 degrees less than the third angle. This can be represented as 2x + 3 - 20, which simplifies to 2x - 17.
Now, we can set up an equation using the sum of the four angles equaling 360 degrees:
x + (3x + 6) + (2x + 3) + (2x - 17) = 360
Simplifying the equation:
8x - 8 = 360
Adding 8 to both sides of the equation:
8x = 368
Dividing both sides by 8:
x = 46
Therefore, the measure of the first angle is 46 degrees. Using this information, we can now find the measure of each angle:
First angle: 46 degrees
Second angle: 3x + 6 = 3(46) + 6 = 144 degrees
Third angle: 2x + 3 = 2(46) + 3 = 95 degrees
Fourth angle: 2x - 17 = 2(46) - 17 = 75 degrees
So, the measure of each angle is:
First angle: 46 degrees
Second angle: 144 degrees
Third angle: 95 degrees
Fourth angle: 75 degrees