By applying the consecutive interior angles theorem, lines CD and EF in the image are not parallel for the given angle measures.
What are parallel lines?
Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
Given the following data:
m∠BPG = 139°
m∠GPC = 95°
m∠BQF = 110°
What is the consecutive interior angles theorem?
The consecutive interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the interior angles that are formed are congruent and each pair of the consecutive interior angles is supplementary.
By applying the consecutive interior angles theorem, we have:
m∠BPG + m∠GPC = 180°
139° + 95° ≠ 180° (not parallel).
m∠BPG + m∠BQF = 180°
139° + 110° ≠ 180° (not parallel).
m∠GPC + m∠BQF = 180°
95° + 110° ≠ 180° (not parallel).
For Part 2.
Given the following data:
m∠BPD = 35°
m∠APG = 115°
m∠EQA = 35°
By applying the consecutive interior angles theorem, we have:
m∠BPD + m∠APG = 180°
35° + 115° ≠ 180° (not parallel).
m∠BPD + m∠EQA = 180°
35° + 35° ≠ 180° (not parallel).
m∠EQA + m∠APG = 180°
35° + 110° ≠ 180° (not parallel).
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