SOLUTION: If two angles are each complementary to the same thirt angles, then the sum of the measures of the three angles is less than 360 degrees? True or false and why if false is it false
Algebra.Com
Question 927802: If two angles are each complementary to the same thirt angles, then the sum of the measures of the three angles is less than 360 degrees? True or false and why if false is it false?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If two angles are each complementary to the same third angles, then the sum of the measures of the three angles is less than 360 degrees? True or false and why if false is it false?
-----
Let the 3rd angle be "x"::
Any complement of x is 90-x.
----
Equation:
x + 2(90-x) < 360 (claim)
x + 180-2x < 360
-x < 180
x > -180
The claim is true for x > 0
----
Answer:: True for all x > 0
----
Example::
Let x = 10 degrees
Complement is 90-x = 80 degrees
---
And 10 + 2(80) = 10 + 160 = 170 degrees which is less than 360
===========
Cheers,
Stan H.
-----------
RELATED QUESTIONS
If two angles are complementary, then the sum of their measures is (answered by vheroli)
Two angles are complementary if the sum of the measures of their angles is 90 degrees.... (answered by solver91311)
If the sum of the measures of two angles is 180 degrees, then the angles are... (answered by Boreal)
true or false two angles are complementary angles if and only if the sum of their... (answered by Fombitz)
Two angles are complementary if the sum of their measures is 90°. Find two complementary... (answered by Zucchini)
Two angles are complementary if the sum of their measures is 90 degrees. Find two... (answered by macston)
Two angles are complementary if the sum of their measures is 90°. Find two complementary... (answered by josgarithmetic)
if two angles are complementary, then the sun of the angles are?
if two angles from a... (answered by Alan3354)
Two angles are complementary if the sum of the measures 90. The measure of the first... (answered by Boreal)