Question

∠vzw and ∠vzy are ____________ angles.
∠vzy measures ____________ °
∠vzw and ∠yzx are ____________ angles.
∠yzx measures ____________ °
∠wzx and ∠yzx are ____________ angles.
∠wzx measures ____________ °
∠vzw = 20°

Explanation:

Step1: Identify ∠VZW & ∠VZY type

These two angles share side ZV and form a straight line, so they are supplementary (linear pair) angles.

Step2: Calculate ∠VZY

A straight line is 180°, so subtract ∠VZW (20°):
$\angle VZY = 180^\circ - 20^\circ = 160^\circ$

Step3: Identify ∠VZW & ∠YZX type

These are opposite angles formed by intersecting lines, so they are vertical angles.

Step4: Calculate ∠YZX

Vertical angles are equal, so:
$\angle YZX = \angle VZW = 20^\circ$

Step5: Identify ∠WZX & ∠YZX type

These two angles share side ZX and form a straight line, so they are supplementary (linear pair) angles.

Step6: Calculate ∠WZX

Subtract ∠YZX (20°) from 180°:
$\angle WZX = 180^\circ - 20^\circ = 160^\circ$

Answer:

∠VZW and ∠VZY are supplementary/linear pair angles.
∠VZY measures $\boldsymbol{160}$ °
∠VZW and ∠YZX are vertical angles.
∠YZX measures $\boldsymbol{20}$ °
∠WZX and ∠YZX are supplementary/linear pair angles.
∠WZX measures $\boldsymbol{160}$ °