Final answer:
To find the measure of corresponding angles given by 23x-5 and 21x+5, set the expressions equal and solve for x. After determining x is 5, substitute it back into either expression to find the measure of the angles, which is 110°.
Step-by-step explanation:
The task of finding the measure of corresponding angles given by expressions 23x-5 and 21x+5 involves setting the two expressions equal to each other because corresponding angles are equal in measure. By solving the equation 23x - 5 = 21x + 5, we can find the value of x, and subsequently determine the measure of each angle.
To solve for x, we first subtract 21x from both sides to get 2x - 5 = 5. Then, we add 5 to both sides to obtain 2x = 10. Finally, by dividing both sides by 2, we find that x = 5. Substituting this value back into either original expression will give us the measure of the angles. Using 23x - 5, we have 23(5) - 5, which equals 115 - 5, giving us a final angle measure of 110°.
This type of problem is common in geometry, where understanding properties of corresponding angles is essential.