Final answer:
The given angles are a pair of consecutive interior angles. Consecutive interior angles add up to 180 degrees. By setting up and solving an equation, we can find the value of the missing angle.
Step-by-step explanation:
In this problem, the given angles are (7x + 13) and (8x + 2). We need to identify the type of angle pair, the relationship, and find the value of the missing angle. The given angles are not described in relation to any particular figure or scenario, so we can assume they are just two angles being compared. Therefore, they are a pair of consecutive interior angles. Consecutive interior angles are formed when a transversal crosses two parallel lines. The relationship between consecutive interior angles is that they are supplementary, meaning they add up to 180 degrees. So, we can set up the equation (7x + 13) + (8x + 2) = 180 and solve for x.
Simplifying the equation, we get 15x + 15 = 180. Subtracting 15 from both sides gives us 15x = 165. Dividing both sides by 15, we find x = 11.
To find the value of the missing angle, we can substitute the value of x back into one of the given angles. Let's use (7x + 13). Plugging in x = 11, we get (7 * 11 + 13) = 90 degrees.