Question 1087595

1) What is the measure of an angle if it is {{{360}}} less than five times its own supplement? 

Two angles are supplementary when they add up to {{{180}}} degrees.

if angle is {{{x}}}, its supplement is {{{180-x}}}

if the measure of an angle if it is {{{360}}} less than {{{five}}}{{{ times}}} its own supplement, we have

{{{x+360=5(180-x)}}}....solve for {{{x}}}

{{{x+360=900-5x}}}

{{{x+5x=900-360}}}

{{{6x=540}}}

{{{x=540/6}}}

{{{x=90}}}-> the angle

{{{180-x=180-90=90}}}->its supplement


2) What is the measure of an angle if it is {{{190}}} less than {{{six}}}{{{ times}}} its own complement? 

Two angles are complementary when they add up to {{{90}}} degrees.

if angle is {{{x}}}, its complement is {{{90-x}}}

if the measure of an angle if it is {{{190}}} less than {{{six}}}{{{ times}}} its own complement, we have

{{{x+190=6(90-x)}}}....solve for {{{x}}}

{{{x+190=540-6x}}}

{{{x+6x=540-190}}}

{{{7x=350}}}

{{{x=350/7}}}

{{{x=50}}}-> the angle

{{{90-x=90-50=40}}} ->its complement