Question

in the given picture, if mt ⊥ rv, and xs ⊥ xe, identify each pair of angles as adjacent, vertical, complementary, supplementary, and/or a linear pair. state all that apply.

1. ∠mxr and ∠txv
2. ∠mxr and ∠vxm
3. ∠sxt and ∠txe
4. ∠rxs and ∠sxe
5. ∠txe and ∠mxe

Explanation:

Step1: Recall angle - pair definitions

Adjacent angles share a common side and a common vertex. Vertical angles are opposite each other when two lines intersect. Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees. A linear - pair is a pair of adjacent angles that are supplementary.

Step2: Analyze ∠MXR and ∠TXV

They are vertical angles as they are opposite each other when lines MT and RV intersect.

Step3: Analyze ∠MXR and ∠VXM

They are adjacent angles as they share a common side (XM) and a common vertex (X). Also, since MT⊥RV, ∠MXR + ∠VXM=90°, so they are complementary.

Step4: Analyze ∠SXT and ∠TXE

They are adjacent angles as they share a common side (XT) and a common vertex (X). Also, since XS⊥XE, ∠SXT + ∠TXE = 90°, so they are complementary.

Step5: Analyze ∠RXS and ∠SXE

They are adjacent angles as they share a common side (XS) and a common vertex (X). Also, ∠RXS+∠SXE = 180° (since they form a straight - line RE), so they are supplementary and form a linear pair.

Step6: Analyze ∠TXE and ∠MXE

They are adjacent angles as they share a common side (XE) and a common vertex (X).

Answer:

1. Vertical
2. Adjacent, Complementary
3. Adjacent, Complementary
4. Adjacent, Supplementary, Linear - pair
5. Adjacent