Think About the Process In the diagram, m∠1 = (119 – y)°, m∠2 = 25°, and m∠3 = (x + 43)°. Write an equation to solve for x and an equation to solve for y. Find the values of x and y.
A. 25 + x + 43 = 90 and 119 – y = 90
B. x + 43 = 90 and 25 + 119 – y = 90
C. 25 + x + 43 = 90 and 119 – y = 180
D. 25 + x + 43 = 180 and 119 – y = 90
x =
To solve for ( x ) and ( y ), we need to analyze the angles in the diagram based on the relationships given.
1. For angle ( x ):
Since ( m∠1 ) and ( m∠2 ) and ( m∠3 ) lie on a straight line, they sum to 180°. The equation representing this is:
[
25 + x + 43 = 180
]
This simplifies to:
[
x + 68 = 180
]
[
x = 180 – 68
]
[
x = 112
]
2. For angle ( y ):
Similarly, angles ( m∠1 ) and ( m∠2 ) also relate and should equal 180° in this context:
[
119 – y + 25 = 180
]
Simplifying this gives:
[
144 – y = 180
]
Solving for ( y ):
[
-y = 180 – 144
]
[
-y = 36
]
[
y = -36
]
The correct equations are:
– For ( x ): ( 25 + x + 43 = 180 )
– For