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Question

Difficulty: EasyLines and Angles

A straight road intersects two parallel train tracks. One of the acute angles formed at an intersection measures 72∘72^\circ. What is the measure of any of the obtuse angles formed by these parallel tracks and the intersecting road, in degrees?

Answer: 108

Answer

108
When a transversal intersects parallel lines, the sum of any acute angle and any obtuse angle formed is always 180∘180^\circ. Subtracting 72∘72^\circ from 180∘180^\circ gives the correct obtuse angle of 108∘108^\circ.

Step-by-Step Solution

1
Identify the relationship between the angles.
The acute and obtuse angles are supplementary.
When a transversal intersects parallel lines, consecutive interior angles (or any adjacent pair of acute and obtuse angles) add up to 180∘180^\circ.
2
Calculate the measure of the obtuse angle.
180∘−72∘=108∘180^\circ - 72^\circ = 108^\circ
Subtracting the given acute angle from 180∘180^\circ yields the supplementary obtuse angle.

Key Concept

Parallel Lines and Transversals
Estimated Time:30s
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Topics

Lines and Angles

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