Find the measure of each angle?

Question

Angle A and B are vertical angles
A = x +3y
B= y+110

Also in this diagram, angles C and D are vertical angles.
C = x-4y
D is not shown in an equation format, but since it is a vertical angle to C, is is also x-4y

Answer 1

easy
as A B are vertical A = B x+3y = y+ 110

x + 2y = 110

A and C sum is 180
2x -y = 180

double the 2nd equation and add with 1st

5x = 470
x = 94
y = 8
A = B = 118
C= D= 62

Answer 2

Since angle A &B are vertical angles, therefore,
A=B i.e. x+3y=y+110
x+2y=110 ..........1)
Also angle A&C are linear pairs,therefore,
A+C=180 i.e. x+3y+x-4y=180
2x-y=180 .............2)
Multiply eq.1) by 2 ,we get
2x+4y=220 ............3)
Subtract eq.2) from eq.3)
(2x+4y)-(2x-y)=220-180
2x+4y-2x+y=40
5y=40
y=8
Substitute the value ofy in eq.1),we get
x+2(8)=110
x=110-16
=94

so A=94+3*8=94+24=118
B=118
C=94-4*8=94-32=62
D=62

Answer 3

ok here's my answer:
Given:
Equation1: angleA=x+3y (given)
Equation2: angleB=y+110 (given)
Equation3: angleC=angleD=x-4y (given)

since angleA and angleB are vertical, angleA is then congruent to angleB.

x+3y=y+110 (angleA=angleB)
x= -2y+110 (equation4)




angleB+angleC=180 (straight line)
so,
(y+110) + (x-4y) = 180
-3y+x = 180-110
x = 3y +70 (Equation5)



equation4 to equation5:
-2y+110 = 3y + 70 (since they are both equal to x)
110 - 70 = 3y + 2y
40 = 5y
8 = y




we now have a value for y. so subsituting it's value to any equation will give the value of x. let's use equation5:

x = 3y + 70
x = 3(8) + 70
x = 24 + 70
x = 94


therefore,

angleA = x + 3y
= 94 + 24
A = 118 degrees

angleB = y + 110
= 8 + 110
B = 118 degrees (same with angleA since they are vertical)

angleC = x - 4y
= 94 - 32
C = 62 degrees

angleA + angleC = 180
118 degrees + 62 degrees = 180

Answer 4

enable x be the degree of the middle perspective. the biggest is comparable to 3 cases the middle perspective, so it quite is 3x. The smallest perspective is 10 stages under the middle perspective, so it quite is x - 10. The sum of the interior angles of a triangle is often a hundred and eighty stages. resolve for x. Smallest + middle + greatest = a hundred and eighty x - 10 + x + 3x = a hundred and eighty 5x - 10 = a hundred and eighty 5x = a hundred ninety x = 38 Smallest = x - 10 = 38 - 10 = 28 greatest = 3x = 3(38) = 114 stages The smallest perspective is 28 stages, the middle perspective is 38 stages, and the biggest perspective is 114 stages.