Answer: x=16, y=10
Step-by-step explanation:
To find the value of x and y, we need to know the angle properties. We know that 8x-14 and 5x+34 are equal to each other because of Alternate Exterior Angles. Now, we also know that 8x-14 and 5y+16 are supplementary angles, meaning they are equal to 180°. To solve, let's first find the value of x.
8x-14=5x+34 [subtract both sides by 5x]
3x-14=34 [add both sides by 14]
3x=48 [divide both sides by 3]
x=16
Now that we know x=16, we can find the value of y.
8x-14+5y+16=180 [plug in x=16]
8(16)-14+5y+16=180 [multiply]
128-14+5y+16=180 [combine like terms]
130+5y=180 [subtract both sides by 130]
5y=50 [divide both sides by 5]
y=10
Now, we know that x=16 and y=10.
