One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 10 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
Don't know what else I can do
http://www.jiskha.com/display.cgi?id=1453947294
just translate into Math
smallest angle --- x°
"One angle in a triangle has a measure that is three times as large as the smallest angle. "
second angle = 3x
" the third angle is 10 degrees more than that of the smallest angle"
third angle = x+10
x + 3x + x+10 = 180
5x = 170
x = 34
smallest angle , we called it x, so 34°
second angle, we called it 3x, so 102°
third angle, we called it x=10, so 44°
check: do they add up to 180 ?
34+102+44 = 180
Let's call the measure of the smallest angle x degrees.
According to the given information:
- One angle in the triangle is three times as large as the smallest angle, so that angle measures 3x degrees.
- The measure of the third angle is 10 degrees more than that of the smallest angle, so that angle measures x + 10 degrees.
The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:
x + 3x + (x + 10) = 180
Combining like terms, the equation becomes:
5x + 10 = 180
Subtracting 10 from both sides, we have:
5x = 170
Dividing both sides by 5, we find:
x = 34
Therefore, the measure of the smallest angle is 34 degrees.
To find the measure of the largest angle, we substitute x = 34 back into the equation for the largest angle:
3x = 3(34) = 102
So, the measure of the LARGEST angle is 102 degrees.
To find the measure of the largest angle in the triangle, we need to determine the measures of all three angles. Let's call the measure of the smallest angle x.
According to the problem, we can determine the measures of the other two angles:
- The measure of one angle is three times as large as the smallest angle. Therefore, this angle measures 3x.
- The measure of the third angle is 10 degrees more than the smallest angle. Therefore, this angle measures x + 10.
In a triangle, the sum of all three angles is always 180 degrees. So, we have the equation:
x + 3x + (x + 10) = 180
Now let's solve for x:
5x + 10 = 180
Subtracting 10 from both sides:
5x = 170
Dividing both sides by 5:
x = 34
Now that we have found the measure of the smallest angle, we can find the measures of the other two angles:
- The measure of the largest angle is three times the smallest angle: 3x = 3 * 34 = 102 degrees.
Therefore, the measure of the largest angle in the triangle is 102 degrees.