Question

Given 2 adjacent angles, ∠ABC and ∠DBC. IF m∠ABC = (4x+2)° and m∠DBC = (3x-7)°. If m∠ABD = 100°, what must be the value of x?

Answer 1

4x + 2 + 3x - 7 = 100

7x - 5 = 100

7x = 105

x = 15

Answer 2

To find the value of x, set up and solve an equation using the given information.

Step-by-step explanation:

To find the value of x, we can set up an equation using the given information. Since ∠ABD is a straight angle (180°), we can write the equation: (4x+2) + (3x-7) = 180. Solving this equation will give us the value of x.

Combining like terms, we get: 7x - 5 = 180.

Adding 5 to both sides, we get: 7x = 185.

Finally, dividing both sides by 7, we find that x = 26.