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New SAT Math - Calculator : Triangles

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Example Questions

Example Question #792 : New Sat

Two parallel lines are intersected by a transversal. If the minor angle of intersection between the first parallel line and the transversal is $36^{\circ}$ , what is the minor angle of intersection between the second parallel line and the transversal?

Possible Answers:

$66^{\circ}$

$36^{\circ}$

$54^{\circ}$

$144^{\circ}$

$18^{\circ}$

Correct answer:

$36^{\circ}$

Explanation:

When a line intersects two parallel lines as a transversal, it always passes through both at identical angles (regardless of distance or length of arc).

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Example Question #181 : Coordinate Geometry

If $\overleftrightarrow{FH} \parallel \overleftrightarrow{AD}$ , $\overline{BE}\perp \overleftrightarrow{GC}$ , and $m\angle HGC=58^\circ$ , what is the measure, in degrees, of $\angle ABE$ ?

Alternate interior angles

Possible Answers:

148

122

Correct answer:

148

Explanation:

The question states that $\overleftrightarrow{FH} \parallel \overleftrightarrow{AD}$ . The alternate interior angle theorem states that if two parallel lines are cut by a transversal, then pairs of alternate interior angles are congruent; therefore, we know the following measure:

$m\angle GCA = 58^\circ$

The sum of angles of a triangle is equal to 180 degrees. The question states that $\overline{BE}\perp \overleftrightarrow{GC}$ ; therefore we know the following measure:

$m \angle BEC = 90^\circ$

Use this information to solve for the missing angle: $\angle EBC$

$180^\circ=m\angle EBC+58^\circ+90^\circ$

$m\angle EBC=32^\circ$

The degree measure of a straight line is 180 degrees; therefore, we can write the following equation:

$180^\circ=m\angle ABE+32^\circ$

$m\angle ABE=148^\circ$

The measure of $\angle ABE$ is 148 degrees.

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Example Question #2 : How To Find An Angle Of A Line

Lines A and B in the diagram below are parallel. The triangle at the bottom of the figure is an isosceles triangle.

Act2

What is the degree measure of angle ?

Possible Answers:

Correct answer:

Explanation:

Since A and B are parallel, and the triangle is isosceles, we can use the supplementary rule for the two angles, and 2x+30 which will sum up to 180 . Setting up an algebraic equation for this, we get 4x+2x+30=180 . Solving for , we get x=25 . With this, we can get either 2(25)+30=80 (for the smaller angle) or 4(25)=100 (for the larger angle - must then use supplementary rule again for inner smaller angle). Either way, we find that the inner angles at the top are 80 degrees each. Since the sum of the angles within a triangle must equal 180, we can set up the equation as 80+80+y=180

y=20 degrees.

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New SAT Math - Calculator : Triangles

Study concepts, example questions & explanations for New SAT Math - Calculator

All New SAT Math - Calculator Resources

Example Questions

Example Question #792 : New Sat

Example Question #181 : Coordinate Geometry

Example Question #2 : How To Find An Angle Of A Line

All New SAT Math - Calculator Resources

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