Question

Which equation can you use to solve for x?

A. 180-x=111
B. x+87=180
C. x+111=180
D. x+87=111

Answer 1

D. Because angle 111 is equal to angle 87 + x (vertical angles are congruent). With that, you can make the equation: 87 + x = 111.

Answer 2

`111^(\circ) =87^(\circ)+x^(\circ)`

Explanation:

Refer the attached figure

Vertical angles : Each of the pairs of opposite angles made by two intersecting lines is called vertical angles.

AB and CD are two intersecting lines at point O.

So, By definition ∠AOC and ∠DOB are the pair of vertical angles .

So, ∠AOC = ∠DOB (vertically opposite angles are equal) -1

We are given ∠AOC = 111° and ∠DOB = 87°+x°

Substitute the values in 1

`111^(\circ) =87^(\circ)+x^(\circ)`

So, an equation can you use to solve for x is
`111^(\circ) =87^(\circ)+x^(\circ)`

So, Option B is correct.