Final answer:
To find the value of x, set the two given angles equal to each other and solve for x. The value of x is -9.
Step-by-step explanation:
To find the value of x, we need to set the two given angles equal to each other and solve for x. So, we have 4x + 7 = 10x + 61. Subtracting 4x from both sides, we get 7 = 6x + 61. Subtracting 61 from both sides, we get -54 = 6x. Dividing both sides by 6, we get -9 = x. Therefore, the value of x is -9.