Question

in the figure shown, t || x and k || w and m∠3 = 20. choose the list which includes all of the other angles that measure 20.
a. 1
b. 7, 9, 14
c. 1, 14, 16
d. 1, 5, 7, 9, 11, 14, 16

Explanation:

Step1: Recall angle - relationships in parallel lines

When two lines are parallel, corresponding angles, alternate - interior angles, and alternate - exterior angles are equal, and vertical angles are equal. Given \(t\parallel x\) and \(k\parallel w\) and \(m\angle3 = 20^{\circ}\).

• Vertical angles: \(\angle3\) and \(\angle1\) are vertical angles, so \(m\angle1=20^{\circ}\).
• Corresponding angles: Since \(t\parallel x\) and \(k\parallel w\), \(\angle3\) and \(\angle9\) are corresponding angles, so \(m\angle9 = 20^{\circ}\).
• Alternate - interior angles: \(\angle3\) and \(\angle14\) are alternate - interior angles, so \(m\angle14=20^{\circ}\).

Answer:

B. 7, 9, 14