Answer:
x=21
Step-by-step explanation:
Hello There!
In order to find the value of x we need to find the value of y
The angle labeled y and the right angle are vertical angles with the angle labeled 5y +10 therefore they are congruent
so y+90=5y+10
step 1 subtract y from each side
5y-y=4y
now we have
90=4y+10
step 2 subtract each side by 10
90-10=80
now we have
80=4y
step 3 divide each side by 4
80/4=20
so y =20
now we plug in y to (5y+10)
5x20=100
100+10=110
So now we can find x
The angle labeled 3x+7 is supplementary with the angle that is equal to 110
meaning that the sum of the two angles equal 180
so 180 = 3x+110+7
step 1 combine like terms
110+117
now we have
180=3x+117
step 2 subtract each side by 117
180-117=63
now we have 3x=63
step 3 divide each side by 3
63/3=21
so we can conclude that x = 21
Answer:
x = 21°
Step-by-step explanation:
y = 180° - 90° - (3x+7)°
y = 83° - 3x
(5y + 10) and (3x + 7) are supplementary angles (their sum is 180°) so:
(5y + 10) + (3x + 7) = 180°
reduce:
5y + 3x = 163°
substitute for y:
5(83° - 3x) + 3x = 163°
415° - 15x + 3x = 163°
reduce:
-12x = -252
divide both sides by -12:
x = 21°
y = 83° - 3(21°) = 20°
check:
(5(20) + 10) + (3(21) + 7) = 180°
110° + 70° = 180°
