Question 215331
if one-half of the complement of an angle plus three-fourths of the supplement of the angle equals 110, find the measure of the angle.
:
Let x = "the angle"
:
"if one-half of the complement of an angle"
.5(90-x)
: 
"three-fourths of the supplement" 
.75(180-x)
:
find the measure of the angle.
:
Write the equation for the statement:
"one-half of the complement of an angle plus three-fourths of the supplement of the angle equals 110,"
:
.5(90-x) + .75(180-x) = 110
45 - .5x + 135 - .75x = 110
180 - 1.25x = 110
180 - 110 = +1.25x
x = {{{70/1.25}}}
x = 56 degrees
;
:
See if this is true in the statement:
one-half of the complement of an angle plus three-fourths of the supplement of the angle equals 110,
.5(90-56) + .75(180-56) =
.5(34) + .75(124) =
17 + 93 = 110