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PSAT Math : How to find the angle of two lines

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Example Questions

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

Pythagoras

Refer to the above figure. You are given that AB = 5 and BC = 12 . Which of the following statements would be sufficient to prove that $\angle 2$ is a right angle, given what is already known?

I) AC = 13

II) $\angle BAC$ and $\angle BCA$ are both acute

III) $\angle 1$ is a right angle

Possible Answers:

II and III only

None of these

I and III only

I, II, and III

I and II only

Correct answer:

I and III only

Explanation:

If AC = 13 , then $\Delta ABC$ has short sides AB = 5 , BC = 12 and long side AC = 13 . Since

$5^{2} + 12^{2} = 25 + 144 = 169 = 13^{2}$ ,

then, by the converse of the Pythagorean Theorem, $\Delta ABC$ is a right triangle with right angle $\angle 2$ . Statement I is sufficient.

If $\angle BAC$ and $\angle BCA$ are both acute,we know nothing about $\angle 2$ ; every triangle has at least two acute angles regardless of type. Statement II tells us nothing.

$\angle 1$ and $\angle 2$ form a linear pair and are therefore supplementary. If one is a right angle, so is the other. Therefore, if $\angle 1$ is a right angle, so is $\angle 2$ . Statement III is sufficient.

The correct response is Statement I and III only.

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Example Question #591 : Geometry

Thingy_5

Note: $m\parallel n$

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

Possible Answers:

$\angle ACB$

$\angle CGH$

$\angle BCG$

$\angle HGJ$

$\angle CGF$

Correct answer:

$\angle HGJ$

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. $\angle DCG$ is formed by the intersection of transversal and ; the angle in the same relative position where intersects is $\angle HGJ$ .

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

Thingy_5

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

Possible Answers:

$\angle HGJ$

$\angle ACB$

$\angle BCG$

$\angle CGH$

$\angle CGF$

Correct answer:

$\angle CGF$

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

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Example Question #271 : Plane Geometry

Thingy_5

Refer to the above diagram.

$\angle ABC$ and which other angle form a pair of vertical angles?

Possible Answers:

$\angle BFG$

$\angle AFY$

$\angle ZBF$

$\angle ACB$

$\angle ZBA$

Correct answer:

$\angle ZBF$

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 $\angle ZBF$ fits both descriptions with $\angle ABC$ .

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PSAT Math : How to find the angle of two lines

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

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

Example Question #591 : Geometry

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

Example Question #271 : Plane Geometry

All PSAT Math Resources

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