4 - identify the angle relationship. only check the options that apply to the given angles.
9) ∠fxd and ∠axf
□ adjacent
□ vertical
□ complementary
□ supplementary
□ linear pair
10) ∠fxe and ∠rxc
□ adjacent
□ vertical
□ complementary
□ supplementary
□ linear pair
11) ∠cxd and ∠dxe
□ adjacent
□ vertical
□ complementary
□ supplementary
□ linear pair
12) ∠axf and ∠exf
□ adjacent
□ vertical
□ complementary
□ supplementary
□ linear pair
13) if ( mangle dxe = 8x - 6 ), find the value of ( x ) so that ( overleftrightarrow{ad} perp overleftrightarrow{re} ).

Question

Accepted Answer

# Explanation:
## Step1: Recall definitions
- **Adjacent angles**: Share a common side and vertex.
- **Vertical angles**: Opposite angles formed by two intersecting lines.
- **Complementary angles**: Sum to $90^{\circ}$.
- **Supplementary angles**: Sum to $180^{\circ}$.
- **Linear pair**: Adjacent and supplementary.

## Step2: Analyze $\angle FXD$ and $\angle AXF$
- They share a common side $XF$ and vertex $X$, so they are adjacent.
- They form a straight line ($\angle AXD = 180^{\circ}$), so they are supplementary.
- Since they are adjacent and supplementary, they are a linear pair.

## Step3: Analyze $\angle FXE$ and $\angle RXC$
- They are opposite angles formed by two intersecting lines, so they are vertical.

## Step4: Analyze $\angle CXD$ and $\angle DXE$
- They share a common side $XD$ and vertex $X$, so they are adjacent.

## Step5: Analyze $\angle AXF$ and $\angle EXF$
- They share a common side $XF$ and vertex $X$, so they are adjacent.

# Answer:
9) adjacent, supplementary, linear pair
10) vertical
11) adjacent
12) adjacent

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QUESTION IMAGE

Question

Explanation:

Step1: Recall definitions

Step2: Analyze \(\angle FXD\) and \(\angle AXF\)

Step3: Analyze \(\angle FXE\) and \(\angle RXC\)

Step4: Analyze \(\angle CXD\) and \(\angle DXE\)

Step5: Analyze \(\angle AXF\) and \(\angle EXF\)

Answer: