PSAT Math : How to find the angle of two lines

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #1 :Lines

Pythagoras

Refer to the above figure. You are given thatand. Which of the following statements would be sufficient to prove thatis a right angle, given what is already known?

I)

II)andare both acute

III)is a right angle

Possible Answers:

II and III only

I and II only

I, II, and III

None of these

I and III only

Correct answer:

I and III only

Explanation:

If, thenhas short sidesand long side. Since

,

then, by the converse of the Pythagorean Theorem,is a right triangle with right angle. Statement I is sufficient.

Ifandare both acute,we know nothing about; every triangle has at least two acute angles regardless of type. Statement II tells us nothing.

andform a linear pair and are therefore supplementary. If one is a right angle, so is the other. Therefore, ifis a right angle, so is. Statement III is sufficient.

The correct response is Statement I and III only.

Example Question #1 :Lines

Thingy_5

Note:

Refer to the above diagram.and which other angle form a pair of corresponding angles?

Possible Answers:

Correct answer:

Explanation:

Two angles formed by a transversal line crossing two other lines are corresponding angles if, relative to the points of intersection, they are in the same position.is formed by the intersection of transversaland; the angle in the same relative position whereintersectsis.

Example Question #1 :How To Find The Angle Of Two Lines

Thingy_5

Refer to the above diagram.and which other angle form a pair of alternate interior angles?

Possible Answers:

Correct answer:

Explanation:

Two angles formed by a transversal line crossing two other lines are alternate interior angles if:

I) Both angles have their interiors between the lines crossed

II) The angles have their interiors on the opposite sides of the transversal.

Of the given choices, only适合description; the interior of each is betweenand, and the interiors are on the opposite sides of.

Example Question #1 :How To Find The Angle Of Two Lines

Thingy_5

Refer to the above diagram.

and which other angle form a pair of vertical angles?

Possible Answers:

Correct answer:

Explanation:

Two angles are vertical angles if they share a vertex, anf if their union is a pair of intersecting lines. Of the five choices, onlyfits both descriptions with.

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