Question

visit www.bigideasmathvideos.com to watch the flipped video instruction for the \try this try this video for extra example 1 - use the properties and theorems of parallel lines to complete the problems below. 1) the measures of three of the numbered angles are 75°. identify the angles. tell which theorem you use in each case.

Explanation:

Step1: Identify ∠2 as 75°

Vertical angles are congruent.
$\angle 2 = 75^\circ$ (vertical to the given $75^\circ$ angle)

Step2: Identify ∠6 as 75°

Corresponding angles are congruent.
$\angle 6 = 75^\circ$ (corresponding to the given $75^\circ$ angle)

Step3: Identify ∠7 as 75°

Alternate interior angles are congruent.
$\angle 7 = 75^\circ$ (alternate interior to the given $75^\circ$ angle)

Answer:

1. $\boldsymbol{\angle 2 = 75^\circ}$; Vertical Angles Congruence Theorem
2. $\boldsymbol{\angle 6 = 75^\circ}$; Corresponding Angles Postulate
3. $\boldsymbol{\angle 7 = 75^\circ}$; Alternate Interior Angles Congruence Theorem