intermediate algebra
posted by sally .
A triangle is such that the largest angle is 11 times the smallest angle. The third angle is 27° less than the largest angle. Find the measure of each angle. (Enter solutions from smallest to largest.)

The largest angle = 11 * the smallest angle
The third angle = The largest angle  27 ° = 11 * the smallest angle  27 °
The angles of a triangle always sum to 180 °
The smallest angle + The largest angle + The third angle = 180 °
The smallest angle + 11 * the smallest angle + 11 * the smallest angle 27 ° = 180°
23 * the smallest angle  27 ° = 180 °
23 * the smallest angle = 180 ° + 27 °
23 * the smallest angle = 207 ° Divide both sides by 23
The smallest angle = 207 ° / 23
The smallest angle = 9 °
The largest angle = 11 * the smallest angle
The largest angle = 11 * 9 °
The largest angle = 99 °
The third angle = The largest angle  27 °
The third angle = 99 °  27 °
The third angle = 72 °
72 ° + 99 ° + 9 ° = 180 °
Respond to this Question
Similar Questions

Algebra
The measure of the largest angle of a certain triangle is 6 times the smallest. The measure of the remaining angle is 100 degrees less than te sum of the other two angles. Write a system of 3 equations you could use to solve this problem. … 
MATH
in a scalene triangle, the measure of the largest angle is four more than two times the smallest and the other angle is two more than the smallest. what is the measure of the largest angle ? 
geomitry
the first angle of a triangle is complementry to the third angle. the second angle is 16 degrees less than five times the first angle. find the measure of the largest angle of the triangle. 
intermediate algebra
A triangle is such that the largest angle is 11 times the smallest angle. The third angle is 27° less than the largest angle. Find the measure of each angle. (Enter solutions from smallest to largest.) 
Algebra
The following problem must be solved 3 different ways in which X=smallest angle for problem 1. Problem 2 would be X=medium sized angle. Problem 3 would start with X=largest angle. I was able to figure out X=smallest angle, but I am … 
Algebra II
The measure of the largest angle of a triangle is 90 more than the measure of the smallest angle, and the measure of the remaining angle is 30 more than the measure of the smallest angle. Find the measure of each angle. Show your … 
Algebra
The measure of the smallest angle of a triangle is onefourth the measure of the largest angle. The measure of the second angle is 36 less than the measure of the largest angle. 
algebra
A triangle is such that the largest angle is 12 times the smallest angle. The third angle is 20 less than the largest angle. Find the measure of each angle. (12x)+ x+20(12x)=180. im having a difficult time setting up the equation 
Algebra
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. 
Algebra
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.