The sum of the measures of angles x and y is 127 degree. If the measure of anglexx is 34 more than half the measure of angle yy, what is the measure of each angle?

2 Answers
Jun 16, 2017

x=65^@,y=62^@x=65,y=62

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=12712y+34+y=127

rArr3/2y+34=12732y+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

Jun 16, 2017

x=65,y=62

Explanation:

Let the measure of angle x be x and angle y be y.

We are given two pieces of information:
x+y=127 .........(1)
x=y/2+34 .........(2)

Substituting (2) into (1) gives
y/2+34+y=127
y=62

Substituting y=62 into (1) gives
x+62=127
x=65

Therefore x=65,y=62