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: Identify angle - relationships

Since \(t\parallel x\) and \(k\parallel w\), we use the properties of parallel lines and transversals. Corresponding angles are equal, alternate - interior angles are equal, and vertical angles are equal. \(\angle3\) and \(\angle11\) are vertical angles, so \(m\angle11 = m\angle3=20\). \(\angle3\) and \(\angle9\) are alternate - interior angles, so \(m\angle9 = m\angle3 = 20\). \(\angle3\) and \(\angle14\) are corresponding angles, so \(m\angle14 = m\angle3=20\).

Answer:

B. 7, 9, 14