Question

1. find all the missing angles ∠1 ∠2 ∠3 ∠4 ∠5 ∠6 ∠7 (diagram with 120° angle, parallel lines, transversal)

Explanation:

Step1: Find ∠5

∠5 and the 120° angle are supplementary (linear pair), so \( \angle 5 = 180^\circ - 120^\circ = 60^\circ \).

Step2: Find ∠1

∠1 and ∠5 are corresponding angles (parallel lines cut by transversal), so \( \angle 1 = \angle 5 = 60^\circ \).

Step3: Find ∠2

∠1 and ∠2 are supplementary (linear pair), so \( \angle 2 = 180^\circ - \angle 1 = 180^\circ - 60^\circ = 120^\circ \).

Step4: Find ∠3

∠3 and ∠1 are vertical angles, so \( \angle 3 = \angle 1 = 60^\circ \).

Step5: Find ∠4

∠4 and ∠2 are vertical angles, so \( \angle 4 = \angle 2 = 120^\circ \).

Step6: Find ∠6

∠6 and the 120° angle are vertical angles, so \( \angle 6 = 120^\circ \).

Step7: Find ∠7

∠7 and ∠5 are vertical angles, so \( \angle 7 = \angle 5 = 60^\circ \).

Answer:

\( \angle 1 = 60^\circ \), \( \angle 2 = 120^\circ \), \( \angle 3 = 60^\circ \), \( \angle 4 = 120^\circ \), \( \angle 5 = 60^\circ \), \( \angle 6 = 120^\circ \), \( \angle 7 = 60^\circ \)