document.write( "Question 328008: if the difference between the measures of two smaller angles of right triangle is 20 degrees, what is the measure , in degrees,of the smallest angle ? \n" ); document.write( "

Algebra.Com's Answer #234884 by jessica43(140) $\"\"$ $\"About$

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To solve this problem, you are going to need to write two equations using what you know.
\n" ); document.write( "First, you know that you have a right triangle. This means that one angle is 90 degrees, and the sum of the two smaller angles must equal 90 degrees (because the sum of the angles of a triangle is 180):
\n" ); document.write( "A + B + C = 180
\n" ); document.write( "90 + B + C = 180
\n" ); document.write( "B + C = 90 (where A is the right angle, B and C are the smaller angles)
\n" ); document.write( "Second, you know that the difference between the measures of the two smaller angles is 20 degrees:
\n" ); document.write( "B - C = 20 (where C is the smallest angle of the triangle)
\n" ); document.write( "This can be rewritten as B = 20 + C
\n" ); document.write( "Now plug in this second equation into the first equation and solve for C:
\n" ); document.write( "B + C = 90
\n" ); document.write( "(20 + C) + C = 90
\n" ); document.write( "20 + 2C = 90
\n" ); document.write( "2C = 70
\n" ); document.write( "C = 35
\n" ); document.write( "So the smallest angle is 35 degrees. \n" ); document.write( "

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