Identifying Angle Pairs:
9. ∠ 1 and ∠8 are Congruent - Corresponding angles.
10. ∠5 and ∠6 are Supplementary - Consecutive interior angles.
11. ∠6 and ∠8 are Supplementary - Consecutive interior angles.
12. ∠ 2 and ∠3 are Supplementary - Linear pair.
13. ∠4 and ∠7 are Congruent - Corresponding angles.
14. ∠3 and ∠6 are Supplementary - Alternate interior angles.
Let's solve for the measures of the angles and then determine the relationships between them.
Given:
![\[ m\angle 3 = 74^\circ \]](https://img.qammunity.org/2022/formulas/mathematics/high-school/vjt6rjdbfnr72pn2nh2wl5uxtzips22fyh.png)
Based on the information provided, here are the measures of the remaining angles:
m∠1 = 74° (given)
m∠2 = 180° - m∠1 = 180° - 74° = 106° (opposite angles in a straight line are supplementary)
m∠4 = 74° (given)
m∠5 = 180° - m∠4 = 180° - 74° = 106° (opposite angles in a straight line are supplementary)
Angle Pair Congruent or Supplementary Classification
1 & 8 Congruent Corresponding angles (formed by parallel lines and a transversal)
5 & 6 Supplementary Consecutive interior angles (formed on the same side of a transversal between two parallel lines)
6 & 8 Supplementary Consecutive interior angles (formed on the same side of a transversal between two parallel lines)
2 & 3 Supplementary Linear pair (form a straight line)
4 & 7 Congruent Corresponding angles (formed by parallel lines and a transversal)
3 & 6 Supplementary Alternate interior angles (formed on opposite sides of a transversal between two parallel lines)