Answer: y = 50
Explanation:
Supplement angles are two angles that sums up to 180°. So we could interfere that (8x - 14)° and (5y + 16)° are supplement angles. But before we move on, we should first solve for x. Opposite angles are equal. So therefore the angle opposite to 8x - 14 is also equal to 8x - 14. Guess what? Corresponding angles are also considered equal. So we could then conclude as following:
5x + 34 = 8x - 14
With the equation above we can now solve for x. We first add 14 on both sides.
5x + 48 = 8x
We then substract 5x on both sides.
48 = 3x
We finally divide 3 on both sides. This gives us the value of x.
x = 16
Now that we know the value of x, we could now solve (8x - 14)°. We first start by substituting in the equation.
8(16) - 14
We then multiply 8 with 16.
128 - 14
We finally substract 14 from 128. This gives now the value of the angle
114°
Now that we know this, we could now solve for y. Like I said earlier, supplement angles add up to 180°. So our equation should go as following:
114 + (5y + 16) = 180
We first add like terms together.
5y + 130 = 180
We then substract 130 on both sides
5y = 50
We finally divide 5 on both sides of the equation.
y = 50