Question

Solve for x
left top corner E
left bottom corner D
Right top corner F
Right bottom corner C
inner top left corner 98°
inner bottom left corner 100°
inner top right corner 9x-8
inner bottom right corner 80°
what is the answer
1
6
2
10

Answer 1

To solve for \( x \) using the information about the angles, we can start by noting that the corners relate to a quadrilateral where the opposite angles are supplementary.

The angles given are:

- Inner top left corner: \( 98^\circ \)
- Inner bottom left corner: \( 100^\circ \)
- Inner top right corner: \( 9x - 8^\circ \)
- Inner bottom right corner: \( 80^\circ \)

1. **First, let's look at the bottom left and bottom right corners:**
\[
100^\circ + 80^\circ = 180^\circ
\]
This confirms that they are supplementary as required.

2. **Now let's look at the top left and top right corners:**
\[
98^\circ + (9x - 8)^\circ = 180^\circ
\]

3. **Now we can set up the equation:**
\[
98 + 9x - 8 = 180
\]

4. **Combine like terms:**
\[
90 + 9x = 180
\]

5. **Isolate \( x \):**
\[
9x = 180 - 90
\]
\[
9x = 90
\]
\[
x = \frac{90}{9}
\]
\[
x = 10
\]

Thus, the solution is:
\[
\boxed{10}
\]