The measured angles are m∠1 = 53°, m∠2 = 72°, m∠3 = 55°, m∠4 = 127°, m∠6 = 55°
Properties of parallel lines
Parallel lines are lines that do not meet.
in geometry, they are normally intersected by lines called transversal.
in such an arrangement the angle formed between the top of one parallel line and the transversal is corresponding and equal to the the angle formed between the top of the second parallel line and the transversal.
Analysis:
∠6 + ∠7 = 180( angles on a straight line sum up to 180°)
but ∠7(given) = 125°
∠6+125 = 180
∠6 = 180 - 125 = 55°
∠4 + ∠5 = 180( sum of angles on a straight line = 180)
but ∠5(given) = 53°
∠4 + 53 = 180°
∠4 = 180 - 53 = 127°
∠2 + ∠5 + ∠6 = 180 ( sum of angles in a triangle is 180)
∠2 + 53 + 55 = 180
∠2 + 108 = 180
∠2 = 180 - 108 = 72°
∠1 = ∠5 ( alternate angles are equal)
∠1 = 53°
∠6 = ∠3 (alternate angles are equal)
∠3 = 55°
In conclusion, the measure angles are m∠1 = 53°, m∠2 = 72°, m∠3 = 55°, m∠4 = 127°, m∠6 = 55°.
Learn more about parallel lines: brainly.com/question/24607467
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