Final answer:
By solving the equation set up due to the congruence of the vertical angles, we find that x equals 15. Plugging this value back into the expressions for the angles, both angles are found to be 122 degrees.
Step-by-step explanation:
The question is about solving for the values of two vertical angles given by the expressions (7x + 17) and (8x + 2)°. Vertical angles are congruent, which means they have equal measures. Therefore, we can set the two expressions equal to each other to solve for x:
7x + 17 = 8x + 2
Now we'll subtract 7x from both sides:
17 = x + 2
Subtract 2 from both sides:
x = 15
Substitute x back into the original expressions to find each angle:
7x + 17 = 7(15) + 17 = 105 + 17 = 122°
8x + 2 = 8(15) + 2 = 120 + 2 = 122°
Both angles measure 122°. Therefore, the answer is (a) 7x+17 and 8x+2.