Question

given: de || af if ∠1 = 60° and ∠3 = 100°, find the measures of the remaining angles in the figure.options:∠2 = 20°, ∠4 = 60°, ∠5 = 100°, ∠6 = 80°;∠2 = 10°, ∠4 = 65°, ∠5 = 105°, ∠6 = 75°;∠2 = 30°, ∠4 = 40°, ∠5 = 110°, ∠6 = 70°;∠2 = 50°, ∠4 = 70°, ∠5 = 60°, ∠6 = 120°

Explanation:

Step1: Find ∠2

Since ∠1, ∠2, and ∠3 are on a straight line, their sum is \(180^\circ\). So, \(\angle 2 = 180^\circ - \angle 1 - \angle 3\). Substituting \(\angle 1 = 60^\circ\) and \(\angle 3 = 100^\circ\), we get \(\angle 2 = 180^\circ - 60^\circ - 100^\circ = 20^\circ\).

Step2: Find ∠4

Because \(DE \parallel AF\), \(\angle 4\) and \(\angle 1\) are alternate interior angles. So, \(\angle 4 = \angle 1 = 60^\circ\).

Step3: Find ∠5

Since \(DE \parallel AF\), \(\angle 5\) and \(\angle 3\) are alternate interior angles. Thus, \(\angle 5 = \angle 3 = 100^\circ\).

Step4: Find ∠6

∠5 and ∠6 are supplementary (they form a linear pair). So, \(\angle 6 = 180^\circ - \angle 5 = 180^\circ - 100^\circ = 80^\circ\).

Answer:

\(\angle 2 = 20^\circ\), \(\angle 4 = 60^\circ\), \(\angle 5 = 100^\circ\), \(\angle 6 = 80^\circ\) (the first option)