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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #1 : How To Find An Angle In A Parallelogram

Vt_rhomb_4

Given that the measurement of angle B=52 degrees, find the sum of angle and angle

Possible Answers:

$104^\circ$

$128^\circ$

$65^\circ$

$256^\circ$

Correct answer:

$256^\circ$

Explanation:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal 360 degrees. And, the adjacent interior angles must be supplementary angles (sum of 180 degrees)--i.e. angles A+D=180 degrees.

The solution to this problem is:

$\measuredangle B+\measuredangle C=180^\circ$

$52+\measuredangle C=180^\circ$

$C= 180-52=128^\circ$

$\measuredangle C=\measuredangle A$

Therefore,

$128+128=256^\circ$

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Example Question #6 : How To Find An Angle In A Parallelogram

Custom_vt_rhomb_3

Using the above rhombus, find the measurement of angle

Possible Answers:

$133^\circ$

$113^\circ$

$47^\circ$

$313^\circ$

Correct answer:

$133^\circ$

Explanation:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal 360 degrees. And, the adjacent interior angles must be supplementary angles (sum of 180 degrees).

Thus, the solution is:

$\measuredangle H+\measuredangle G=180^\circ$
$47+\measuredangle G=180^\circ$
$\measuredangle G=180-47=133^\circ$

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Example Question #1 : How To Find An Angle In A Parallelogram

Vt_rhomb_4

In the above rhombus, angle has a measurement of 128 degrees. Find the sum of angles and

Possible Answers:

$128^\circ$

$104^\circ$

$78^\circ$

$52^\circ$

Correct answer:

$104^\circ$

Explanation:

128+D=180

D=180-128=52

$\measuredangle D=\measuredangle B$

Thus,

$52+52=104^\circ$

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Example Question #8 : How To Find An Angle In A Parallelogram

Vt_parallelogram_5

Using the parallelogram above, find the measurement of angle

Possible Answers:

$91^\circ$

$162^\circ$

$81^\circ$

$80^\circ$

Correct answer:

$81^\circ$

Explanation:

A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal 360 degrees. And, the adjacent interior angles must be supplementary angles (sum of 180 degrees).

Since, angle and are supplementary the solution is:

$180-99=81^\circ$

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Example Question #1 : How To Find An Angle In A Parallelogram

Vt_parallelogram_5

Using the parallelogram above, find the sum of angles and .

Possible Answers:

$80^\circ$

$99^\circ$

$162^\circ$

$81^\circ$

Correct answer:

$162^\circ$

Explanation:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal 360 degrees. And, the adjacent interior angles must be supplementary angles (sum of 180 degrees).

The first step to solving this problem is to find the measurement of angle . Since angle is a supplementary angle to angle , angle

$180-99=81^\circ$

Since, angle and are opposite interior angles they must be equivalent.

Thus, the final solution is:

$81+81=162^\circ$

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Example Question #1 : How To Find An Angle In A Parallelogram

Vt_parallelogram_5

Using the parallelogram above, find the sum of angles and .

Possible Answers:

$162^\circ$

$198^\circ$

$81^\circ$

$99^\circ$

Correct answer:

$198^\circ$

Explanation:

A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal 360 degrees. And, the adjacent interior angles must be supplementary angles (sum of 180 degrees).

Since, angles and are opposite interior angles, they must be equivalent.

Therefore, the solution is:

$99+99=198^\circ$

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Example Question #11 : How To Find An Angle In A Parallelogram

Parallelogram_7

In the parallelogram shown above, angle is degrees. Find the measure of angle

Possible Answers:

$144^\circ$

$90^\circ$

$92^\circ$

$72^\circ$

Correct answer:

$72^\circ$

Explanation:

A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal 360 degrees. And, the adjacent interior angles must be supplementary angles (sum of 180 degrees).

Since, angles and are opposite interior angles, thus they must be equivalent.

$\measuredangle E=72^\circ$ , therefore $\measuredangle G=72^\circ$

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Example Question #11 : How To Find An Angle In A Parallelogram

Parallelogram_7

In the parallelogram shown above, angle is degrees. Find the sum of angles and .

Possible Answers:

$140^\circ$

$216^\circ$

$126^\circ$

$104^\circ$

Correct answer:

$216^\circ$

Explanation:

A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal 360 degrees. And, the adjacent interior angles must be supplementary angles (sum of 180 degrees).

Thus, the solution is:

$180-72=108^\circ$

Since both angles and equal 108. There sum must equal $108+108=216^\circ$

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Example Question #13 : How To Find An Angle In A Parallelogram

Parallelogram_7

Using the parallelogram above, find the sum of angles and

Possible Answers:

$180^\circ$

$90^\circ$

$270^\circ$

Not enough information is provided to find an answer.

Correct answer:

$180^\circ$

Explanation:

A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal 360 degrees.

Also, the adjacent interior angles must be supplementary angles (sum of 180 degrees).

Since, angles and are adjacent to each other they must be supplementary angles.

Thus, the sum of these two angles must equal 180 degrees.

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Example Question #31 : Parallelograms

A paralellogram as two angles that are 65 degrees and 115 degrees respectively. What are the other two angles in the paralellogram?

Possible Answers:

$180^{\circ} \text{and} \; 360^{\circ}$

$25^{\circ} \text{and} \; 65^{\circ}$

$65^{\circ} \text{and} \; 115^{\circ}$

$50^{\circ} \text{and} \; 65^{\circ}$

$\text {Not enough information}$

Correct answer:

$65^{\circ} \text{and} \; 115^{\circ}$

Explanation:

This question is very simple to answer if you remember that ALL paralellograms have two pairs of equal and opposite angles, and that the four angles in any quadrilateral MUST add up to 360 degrees.

Because the angles given are different, we know that they are supplementary and the other two missing angles MUST be the same.

$65^{\circ} + 115^{\circ} + 65^{\circ} + 115^{\circ} = 360^{\circ}$

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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : How To Find An Angle In A Parallelogram

Example Question #6 : How To Find An Angle In A Parallelogram

Example Question #1 : How To Find An Angle In A Parallelogram

Example Question #8 : How To Find An Angle In A Parallelogram

Example Question #1 : How To Find An Angle In A Parallelogram

Example Question #1 : How To Find An Angle In A Parallelogram

Example Question #11 : How To Find An Angle In A Parallelogram

Example Question #11 : How To Find An Angle In A Parallelogram

Example Question #13 : How To Find An Angle In A Parallelogram

Example Question #31 : Parallelograms

All Intermediate Geometry Resources

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