The sum of the measures of angles x and y is 127 degree. If the measure of anglex∠x is 34 more than half the measure of angle y∠y, what is the measure of each angle?
2 Answers
Explanation:
"we can write the following equations from the statements"we can write the following equations from the statements
x+y=127to(1)x+y=127→(1)
x=1/2y+34to(2)x=12y+34→(2)
"substitute " (2)" into " (1)substitute (2) into (1)
rArr1/2y+34+y=127⇒12y+34+y=127
rArr3/2y+34=127⇒32y+34=127
"subtract 34 from both sides"subtract 34 from both sides
3/2ycancel(+34)cancel(-34)=127-34
rArr3/2y=93
rArry=93/(3/2)=93xx2/3=62
"substitute this value into " (1)" and solve for x"
x+62=127rArrx=65
rArrx=65^@" and " y=62^@
color(blue)"As a check " 62+65=127
Explanation:
Let the measure of angle x be
We are given two pieces of information:
Substituting (2) into (1) gives
Substituting
Therefore