Answer:
The answer is x = 26 and y = 31.
Step-by-step explanation:
To solve this problem, we should first solve for the value of x. Since the angles that measure (5x-17) and (3x-11) are supplementary, this means that they must add up to 180 degrees. This allows us to make the following equation:
(5x - 17) + (3x-11) = 180
When we combine like terms on the left side of the equation, we get:
8x - 28 = 180
Then, we can add 28 to both sides.
8x = 208
Finally, we can divide both sides by 8 to get x alone on the left side of the equation.
x = 26
Now that we know our value for x, we must find our value for y. To do this, we should notice that the angle 3x-11 has a vertical angle (an angle that is directly across from it). By the definition of vertical angles, this angle must have the same measure, meaning it will also have the value 3x - 11. This vertical angle is complementary to the angle 2y + 5, which means that their sum must equal 90 degrees; therefore, we can make the following equation:
3x - 11 = 2y + 5
Since we found our value of x already in the above equation, we can substitute this value into this equation:
3(26) - 11 = 2y + 5
Next, we can perform the multiplication on the left side of the equation.
78 - 11 = 2y + 5
Then, we can perform the subtraction on the left side of the equation.
67 = 2y + 5
Next, we should subtract 5 from both sides of the equation.
62 = 2y
Finally, we should divide both sides of the equation by 2 to get the variable y by itself on the right side of the equation.
y = 31
Therefore, the answer to this problem is x = 26 and y = 31.
Hope this helps!
