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 that  and . Which of the following statements would be sufficient to prove that  is a right angle, given what is already known?

I) 

II)  and  are 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 , then  has short sides  and long side . Since

,

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

 

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

 

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

 

The correct response is Statement I and III only.

Example Question #592 : Geometry

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 transversal  and ; the angle in the same relative position where  intersects  is .

Example Question #592 : Psat Mathematics

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  fits the description; the interior of each is between  and , and the interiors are on the opposite sides of .

Example Question #1 : 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, only  fits both descriptions with .

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