SOLUTION: The measure of one acute angle of an obtuse triangle is 10 degrees more than the measure of the other acute angle. The possible measures of the smaller acute angle are: (1) > 40

Algebra ->  Triangles -> SOLUTION: The measure of one acute angle of an obtuse triangle is 10 degrees more than the measure of the other acute angle. The possible measures of the smaller acute angle are: (1) > 40      Log On


   

Question 105661: The measure of one acute angle of an obtuse triangle is 10 degrees more than the measure of the other acute angle. The possible measures of the smaller acute angle are:
(1) > 40 degrees
(2) = 40 degrees
(3) < 40 degrees
(4) not determinable
SHOW WORK!
PLEASE HELP!!!!! (:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
What do you know?
Let's name the angles of the obtuse triangle, A%5B1%5D,+A%5B2%5D, and O.
A%5B1%5D and A%5B2%5D are acute angles.
O is the obtuse angle.
As with any triangle,
1.+A1%2BA2%2BO=180
Since O is obtuse
2.O%3E90
From 1,
A%5B1%5D%2BA%5B2%5D%2BO=180
O=180-A%5B1%5D-A%5B2%5D
2.O%3E90
%28180-A%5B1%5D-A%5B2%5D%29%3E90
3.A%5B1%5D%2BA%5B2%5D%3C90
You also have a relationship between the acute angles.
Let A%5B1%5D be the smaller angle, and A%5B2%5D be the larger angle.
A%5B2%5D+=+A%5B1%5D+%2B+10
3.A%5B1%5D%2BA%5B2%5D%3C90
A%5B1%5D%2B%28A%5B1%5D%2B10%29%3C90
2A%5B1%5D%3C80
A%5B1%5D%3C40
The answer is 3.