In any triange, the sum of the measures of the angles is 180degrees. In triangle ABC, angle A is four times as large as angle B. Angle C measures 20degrees less than angle B. Find the measure of each angle.
ANSWER
A = 133.333333
B = 33.3333333
C = 13.3333333
WORK
A = 4B
C = B-20
A + B + C = 180
| | | |
(4B) + B (B-20) = 180
\ | /
\ | /
\ | /
\ | /
\ | /
\|/
6B - 20 = 180
B = 33.33333
^
A is 4 times that
C is 20 less than that
Sorry about the lines, I was expecting it to look like this:
img517.imageshack.us/img517/9280/picture1in2.png
Thanks Bartholomew!
in a triangle the sum of the angle is 180degrees. if angle A is three times angle B and Angle C is 10 degrees more than twice Angle A. Find the measures of the three anges to the newarest degree
To find the measure of each angle in triangle ABC, we can set up a system of equations based on the given information.
Let's assume that the measure of angle B is x degrees.
From the given information, we know that angle A is four times as large as angle B, so angle A is 4x degrees.
We also know that angle C measures 20 degrees less than angle B, so angle C is (x - 20) degrees.
Now, we can use the fact that the sum of the measures of the angles in a triangle is 180 degrees to set up an equation:
A + B + C = 180
Substituting the values we found earlier:
4x + x + (x - 20) = 180
Combining like terms:
6x - 20 = 180
Adding 20 to both sides:
6x = 200
Dividing both sides by 6:
x = 33.33
Since angle B cannot have a fractional degree, we can round it to the nearest whole number: x ≈ 33.
Now, we can find the measure of each angle:
Angle A = 4x = 4 * 33 ≈ 132 degrees
Angle B = x ≈ 33 degrees
Angle C = x - 20 ≈ 33 - 20 ≈ 13 degrees
Therefore, the measure of angle A is approximately 132 degrees, angle B is approximately 33 degrees, and angle C is approximately 13 degrees.