Question 1130180

 Suppose that {{{CAT}}} and {{{RAP }}}are vertical angles,
 {{{CAT= 6x-15}}}, and
{{{RAP= 4x+6}}} 

Part A: Draw {{{CAT}}} and {{{RAP}}}.


{{{ drawing( 600, 600, -10, 10, -10, 10,
circle(0,3,4),locate(0.3,3.1,A),locate(-1.5,7.3,C),locate(2.6,6.3,T),
locate(1.5,-1,R),locate(-2.9,0.6,P),
 graph( 600, 600, -10, 10, -10, 10, -3x+3, x+3)) }}}



The angles opposite each other when two lines cross. They are {{{always}}} {{{equal}}}.

then,  {{{CAT=RAP}}}

so, we have:

{{{6x-15=4x+6}}}

{{{6x-4x=15+6}}}

{{{2x=21}}}

{{{x=21/2}}}


=> {{{CAT= 6x-15}}} => {{{CAT= 6(21/2)-15}}} => {{{CAT= 3*21-15 }}}=> {{{CAT= 48}}}
=> {{{RAP=48}}}
 

Part B: Determine the {{{CAT}}} and {{{TAP}}}. 

{{{CAT=TAP}}} are always {{{equal}}} (they are {{{vertical}}} angles)

{{{CAT + TAP=360-( CAT+RAP)}}}...since {{{CAT=TAP}}} , we have

{{{2CAT =360-( 48+48)}}}

{{{2CAT =360-96}}}

{{{2CAT =264}}}

{{{CAT =264/2}}}

{{{CAT =132}}}

=>{{{TAP=132}}}