What is the Value of x+y ? PLZ Help ASAP

ANSWER

[tex]x + y = 60[/tex]

EXPLANATION

Method 1

Vertically opposite angles are equal, therefore

[tex]3x + 55 = 85[/tex]

This implies that,

[tex]3x = 85 - 55[/tex]

We simplify to get,

[tex]3x = 30[/tex]

Dividing through by 3 gives,

[tex]x = 10[/tex]

Also,

[tex]2y - 5 = 95[/tex]

This implies that,

[tex]2x = 95 + 5[/tex]

We simplify the right hand side to get,

[tex]2x = 100[/tex]

We divide both sides both sides by 2 to get,

[tex]x = 50[/tex]

[tex]x + y = 50 + 10[/tex]

[tex]x + y = 60[/tex]

Method 2

Angles on straight line sums to 180°.

[tex]2y-5+85=180[/tex]

This implies that,

[tex]2y+80=180[/tex]

[tex]2y=180-80[/tex]

[tex]2y=100[/tex]

[tex]y=50[/tex]

Also,

[tex]3x+55+95=180[/tex]

[tex]3x+150=180[/tex]

[tex]3x=180-150[/tex]

[tex]3x=30[/tex]

[tex]x=10[/tex]

[tex]x+y=50+10[/tex]

[tex]x+y=60[/tex]

alinakincsem alinakincsem · Answer 2 · 2018-12-14T19:40:32+01:00

Answer:

x + y = 60

Step-by-step explanation:

In the given figure, we have two lines that intersect each other at one point.

Therefore, the opposite angles are equal to each other and we can write them in the form of an equation as:

2y - 5 = 95 --- (1)

3x + 55 = 85 --- (2)

Now solving each of the equations to find the value of x and y.

For y:

2y - 5 = 95

2y = 95 + 5

2y = 100

y = 50

For x:

3x + 55 = 85

3x = 85 -55

3x = 30

x = 10

Therefore, x + y = 10 + 50 = 60.