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Someone please help me with this

Someone please help me with this-example-1
User Goofyahead
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1 Answer

25 votes
25 votes

Answer:

x = 30°, y = 80°

x = 40°, y = 50°

Explanation:

Alternate Interior Angles Theorem

If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.

Therefore, as the two horizontal lines are parallel:

⇒ x = 30°

Exterior Angle Theorem

The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

⇒ y = 50° + x°

⇒ y = 50° + 30°

⇒ y = 80°

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Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Therefore, the angles marked red on the attached diagram are equal.

This means that the two triangles outlined in green are similar.

If two triangles are similar, their corresponding angles are congruent.

⇒ x = 40°.

Interior Angles of a Triangle

The interior angles of a triangle sum to 180°.

Therefore:

⇒ 90° + x + y = 180°

⇒ 90° + 40° + y = 180°

⇒ 130° + y = 180°

⇒ y = 50°

Someone please help me with this-example-1
User Josh Kupershmidt
by
3.1k points