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

##### 2 Answers

Jun 16, 2017

#### Explanation:

#"we can write the following equations from the statements"#

#x+y=127to(1)#

#x=1/2y+34to(2)#

#"substitute " (2)" into " (1)#

#rArr1/2y+34+y=127#

#rArr3/2y+34=127#

#"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

#### Explanation:

Let the measure of angle x be

We are given two pieces of information:

Substituting (2) into (1) gives

Substituting

Therefore