Question

review - test on parallels with angles
identify the type of angle pair from the picture.

1. ∠1 and ∠9 _____________
2. ∠10 and ∠11 _____________
3. ∠11 and ∠23 _____________
4. ∠3 and ∠8 _____________
5. ∠8 and ∠12 _____________
6. ∠21 and ∠20 _____________
7. ∠15 and ∠16_____________
8. ∠2 and ∠7 _____________
9. ∠16 and ∠24_____________
10. ∠6 and ∠17_____________

if j∥k and m∠1 = 92°, find the measures
of the rest of the angles in the figure.
m∠2 = ____ m∠6 = ____
m∠3 = ____ m∠7 = ____
m∠4 = ____ m∠8 = ____
m∠5 = ______

Explanation:

Step1: Identify angle relationships for the first part

• ∠1 and ∠9: Corresponding angles (they are in the same relative position at each intersection where a straight line crosses two others).
• ∠10 and ∠11: Adjacent angles (they have a common side and a common vertex).
• ∠11 and ∠23: Alternate exterior angles (they lie outside the two lines and on opposite sides of the transversal).
• ∠3 and ∠8: No specific standard pair (not corresponding, alternate - interior/exterior, or consecutive - interior).
• ∠8 and ∠12: Alternate interior angles (they lie between the two lines and on opposite sides of the transversal).
• ∠21 and ∠20: Adjacent angles (they have a common side and a common vertex).
• ∠15 and ∠16: Adjacent angles (they have a common side and a common vertex).
• ∠2 and ∠7: No specific standard pair (not corresponding, alternate - interior/exterior, or consecutive - interior).
• ∠16 and ∠24: Corresponding angles (they are in the same relative position at each intersection where a straight line crosses two others).
• ∠6 and ∠17: No specific standard pair (not corresponding, alternate - interior/exterior, or consecutive - interior).

Step2: Calculate angle measures for the second part

Given \(m\angle1 = 92^{\circ}\) and \(j\parallel k\)

• \(m\angle2\): \(\angle1\) and \(\angle2\) are supplementary (\(\angle1+\angle2 = 180^{\circ}\)), so \(m\angle2=180 - 92=88^{\circ}\)
• \(m\angle3\): \(\angle1\) and \(\angle3\) are vertical angles, so \(m\angle3 = m\angle1=92^{\circ}\)
• \(m\angle4\): \(\angle2\) and \(\angle4\) are vertical angles, so \(m\angle4 = m\angle2=88^{\circ}\)
• \(m\angle5\): \(\angle1\) and \(\angle5\) are corresponding angles (since \(j\parallel k\)), so \(m\angle5 = m\angle1=92^{\circ}\)
• \(m\angle6\): \(\angle5\) and \(\angle6\) are supplementary (\(\angle5+\angle6 = 180^{\circ}\)), so \(m\angle6=180 - 92=88^{\circ}\)
• \(m\angle7\): \(\angle5\) and \(\angle7\) are vertical angles, so \(m\angle7 = m\angle5=92^{\circ}\)
• \(m\angle8\): \(\angle6\) and \(\angle8\) are vertical angles, so \(m\angle8 = m\angle6=88^{\circ}\)

Answer:

1. Corresponding angles
2. Adjacent angles
3. Alternate exterior angles
4. No specific standard pair
5. Alternate interior angles
6. Adjacent angles
7. Adjacent angles
8. No specific standard pair
9. Corresponding angles
10. No specific standard pair

\(m\angle2 = 88^{\circ}\), \(m\angle3=92^{\circ}\), \(m\angle4 = 88^{\circ}\), \(m\angle5=92^{\circ}\), \(m\angle6 = 88^{\circ}\), \(m\angle7=92^{\circ}\), \(m\angle8 = 88^{\circ}\)