Question

name two pairs of adjacent angles and two pairs of vertical angles in the figure. (section 7.1) 1. figure with lines intersecting at q, labeled p, r, t, s 2. figure with lines intersecting at u, labeled y, z, v, x, w

Explanation:

Adjacent angles share a common side and vertex, no overlap. Vertical angles are opposite, formed by intersecting lines.

For Figure 1 (intersecting at Q):

1. Adjacent angles: Share a side/vertex. ∠PQR and ∠RQS share side QR and vertex Q; ∠RQS and ∠SQT share side QS and vertex Q.
2. Vertical angles: Opposite each other. ∠PQR and ∠TQS are opposite; ∠PQT and ∠RQS are opposite.

For Figure 2 (intersecting at U):

1. Adjacent angles: Share a side/vertex. ∠YUX and ∠XUZ share side UX and vertex U; ∠XUZ and ∠ZUW share side UZ and vertex U.
2. Vertical angles: Opposite each other. ∠YUV and ∠XUW are opposite; ∠YUX and ∠VUW are opposite.

Answer:

Figure 1:

• Adjacent angles: ∠PQR & ∠RQS, ∠RQS & ∠SQT
• Vertical angles: ∠PQR & ∠TQS, ∠PQT & ∠RQS

Figure 2:

• Adjacent angles: ∠YUX & ∠XUZ, ∠XUZ & ∠ZUW
• Vertical angles: ∠YUV & ∠XUW, ∠YUX & ∠VUW