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High School Math : Plane Geometry

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Example Questions

Example Question #11 : Geometry

$\dpi{100} \small \overline{AB}$ is a straight line. $\dpi{100} \small \overline{CD}$ intersects $\dpi{100} \small \overline{AB}$ at point $\dpi{100} \small E$ . If $\dpi{100} \small \angle AEC$ measures 120 degrees, what must be the measure of $\dpi{100} \small \angle BEC$ ?

Possible Answers:

$\dpi{100} \small 65$ degrees

$\dpi{100} \small 60$ degrees

$\dpi{100} \small 75$ degrees

$\dpi{100} \small 70$ degrees

None of the other answers

Correct answer:

$\dpi{100} \small 60$ degrees

Explanation:

$\dpi{100} \small \angle AEC$ & $\dpi{100} \small \angle BEC$ must add up to 180 degrees. So, if $\dpi{100} \small \angle AEC$ is 120, $\dpi{100} \small \angle BEC$ (the supplementary angle) must equal 60, for a total of 180.

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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 #1 : How To Find The Perimeter Of A Hexagon

What is the perimeter of a regular hexagon with a side length of 12?

Possible Answers:

Correct answer:

Explanation:

To find the perimeter of a regular hexagon you must first know the number of sides in a hexagon which is 6.

When you know the number of sides of a regular polygon to find the perimeter you must multiply the side length by the number of sides.

In this case it is 6*12=72

The answer for the perimeter is .

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Example Question #1 : Hexagons

How many degrees is the interior angle of any regular hexagon?

Possible Answers:

120^o

160^o

90^o

60^o

Correct answer:

120^o

Explanation:

$interior\ angle=\frac{(n-2)*180^o}{n}$

To find the angle of any regular polygon, you find the number of sides, . In this example n=6 .

$interior\ angle=\frac{(n-2)*180^o}{n}=\frac{(6-2)*180^o}{6}$

You then subtract from the number of sides, yielding .

Take and multiply it by 180^o to yield the total number of degrees in the regular hexagon.

(n-2)*180^o=4*180^o=720^o

Then, to find one individual angle, we divide 720^o by the total number of angles, .

$\frac{720^o}{6}=120^o$

The answer is 120^o .

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Example Question #1 : How To Find The Perimeter Of A Hexagon

What is the perimeter of a hexagon with a side length of ?

Possible Answers:

Correct answer:

Explanation:

To find the perimeter of a regular polygon, we take the length of each side, , and multiply it by the number of sides, .

P=s*l

In a hexagon the number of sides is , and in this example the side length is .

P=6*4=24

The perimeter is .

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Example Question #1 : How To Find The Perimeter Of A Hexagon

How many lines of symmetry can be found in a regular hexagon?

Possible Answers:

$\infty$

Correct answer:

Explanation:

The number of lines of symmetry through a regular polygon is equal to the number of sides.

A hexagon has lines of symmetry through each vertex, giving three lines of symmetry that each connect two opposite vertices. The other three lines pass through the midpoints of opposite sides of the hexagon.

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Example Question #2 : How To Find The Perimeter Of A Hexagon

What is the perimeter of a regular hexagon with a side length of ?

Possible Answers:

Correct answer:

Explanation:

To find the perimeter of a regular hexagon you must first know the number of sides in a hexagon which is .

When you know the number of sides of a regular polygon to find the perimeter you must multiply the side length by the number of sides.

In this case it is 6*12=72

The answer for the perimeter is .

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Example Question #1 : How To Find The Perimeter Of A Hexagon

This figure is a regular hexagon with one side measuring 6 cm. Hexagon

What is the perimeter of the regular hexagon in centimeters?

Possible Answers:

Correct answer:

Explanation:

The perimeter of a regular hexagon is just the sum of all 6 sides. Because it's a regular hexagon, the perimemter is just six times one side (6 cm) or 36 cm.

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Example Question #1 : How To Find The Length Of The Diagonal Of A Hexagon

What is the length of a diagonal of a regular hexagon with side length ?

Possible Answers:

5.7

11.4

Correct answer:

Explanation:

Regular hexagons are comprised of six equilateral triangles; in our question, these triangles each have side length 4 (see diagram).

Hectagon

The length of a diagonal is equal to two times the length of the side. In this instance, the answer is 8.

2*4=8

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Example Question #1 : Hexagons

How many diagonals are there in a regular hexagon?

Possible Answers:

Correct answer:

Explanation:

A diagonal is a line segment joining two non-adjacent vertices of a polygon. A regular hexagon has six sides and six vertices. One vertex has three diagonals, so a hexagon would have three diagonals times six vertices, or 18 diagonals. Divide this number by 2 to account for duplicate diagonals between two vertices. The formula for the number of vertices in a polygon is:

$\frac{n\cdot (n-3)}{2}$

where $n=\#\ of\ sides$ .

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High School Math : Plane Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #11 : Geometry

Example Question #181 : Coordinate Geometry

Example Question #1 : How To Find The Perimeter Of A Hexagon

Example Question #1 : Hexagons

Example Question #1 : How To Find The Perimeter Of A Hexagon

Example Question #1 : How To Find The Perimeter Of A Hexagon

Example Question #2 : How To Find The Perimeter Of A Hexagon

Example Question #1 : How To Find The Perimeter Of A Hexagon

Example Question #1 : How To Find The Length Of The Diagonal Of A Hexagon

Example Question #1 : Hexagons

All High School Math Resources

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