Question

angle relationships worksheet #2
a. fill in the correct angle.

1. ∠axe and ____ are vertical angles.
2. ∠axf and ____ are supplementary angles.
3. ∠dxc and ____ are complementary angles.
4. ____ and ∠axb are adjacent angles.
5. ____ and ∠cxd are supplementary angles.
6. ____ and ∠axc are vertical angles.

Explanation:

Step1: Identify vertical angles

Vertical angles are opposite, equal angles formed by intersecting lines. $\angle AXE$ and $\angle DXF$ are opposite each other at vertex $X$.

Step2: Identify supplementary angles

Supplementary angles sum to $180^\circ$. $\angle AXF$ and $\angle AXE$ form a straight line, so they are supplementary.

Step3: Identify complementary angles

Complementary angles sum to $90^\circ$. $\angle DXC$ and $\angle AXE$: since $\angle AXB=90^\circ$, $\angle AXE + \angle EXB=90^\circ$, and $\angle EXB=\angle DXC$ (vertical angles), so $\angle DXC + \angle AXE=90^\circ$.

Step4: Identify adjacent angles

Adjacent angles share a side/vertex. $\angle AXB$ and $\angle BXC$ share side $XB$ and vertex $X$.

Step5: Identify supplementary angles

Supplementary angles sum to $180^\circ$. $\angle AXD$ and $\angle CXD$ form a straight line, so they are supplementary.

Step6: Identify vertical angles

Vertical angles are opposite, equal angles. $\angle EXF$ and $\angle AXC$ are opposite each other at vertex $X$.

Answer:

1. $\angle DXF$
2. $\angle AXE$
3. $\angle AXE$
4. $\angle BXC$
5. $\angle AXD$
6. $\angle EXF$