document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #563264 by stanbon(75887) $\"\"$ $\"About$

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?
\n" ); document.write( "-----
\n" ); document.write( "Let the 3rd angle be \"x\"::
\n" ); document.write( "Any complement of x is 90-x.
\n" ); document.write( "----
\n" ); document.write( "Equation:
\n" ); document.write( "x + 2(90-x) < 360 (claim)
\n" ); document.write( "x + 180-2x < 360
\n" ); document.write( "-x < 180
\n" ); document.write( "x > -180
\n" ); document.write( "The claim is true for x > 0
\n" ); document.write( "----
\n" ); document.write( "Answer:: True for all x > 0
\n" ); document.write( "----
\n" ); document.write( "Example::
\n" ); document.write( "Let x = 10 degrees
\n" ); document.write( "Complement is 90-x = 80 degrees
\n" ); document.write( "---
\n" ); document.write( "And 10 + 2(80) = 10 + 160 = 170 degrees which is less than 360
\n" ); document.write( "===========
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( "----------- \n" ); document.write( "

\n" );