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Intermediate Geometry : How to find an angle in a parallelogram

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Example Questions

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

A parallelogram contains 2 angles measuring 135 and 45. What are the measures of the other 2 angles?

Possible Answers:

60,120

80,100

45,135

Any pair of numbers which add to 180

90,90

Correct answer:

45,135

Explanation:

Parallelograms have angles totalling 360 degrees, but also have matching pairs of angles at the ends of diagonals. Therefore the 2 additional angles must match the 2 given in the question.

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

Rhombus_with_missing_angles_

Using the above rhombus, find the measurement of angle

Possible Answers:

$70^\circ$

$180^\circ$

$110^\circ$

$50^\circ$

Correct answer:

$70^\circ$

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.

Thus, the solution is:

110+ $\measuredangle D=180$

$\measuredangle D=180-110=70$

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Example Question #3 : How To Find An Angle In A Parallelogram

Rhombus_with_missing_angles_

Using the above rhombus, find the measurement of angle .

Possible Answers:

$60^\circ$

$70^\circ$

$110^\circ$

$55^\circ$

Correct answer:

$110^\circ$

Explanation:

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Example Question #4 : How To Find An Angle In A Parallelogram

Custom_vt_rhomb_3

Using the above rhombus, find the sum of angle and angle .

Possible Answers:

$133^\circ$

$94^\circ$

$47^\circ$

$90^\circ$

Correct answer:

$94^\circ$

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:

$\measuredangle H=47^\circ$

$\measuredangle F=47^\circ$

$47^\circ+47^\circ=94^\circ$

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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:

$65^\circ$

$104^\circ$

$256^\circ$

$128^\circ$

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 #21 : Parallelograms

Custom_vt_rhomb_3

Using the above rhombus, find the measurement of angle

Possible Answers:

$313^\circ$

$47^\circ$

$113^\circ$

$133^\circ$

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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Intermediate Geometry : How to find an angle in a parallelogram

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 #1 : How To Find An Angle In A Parallelogram

Example Question #3 : How To Find An Angle In A Parallelogram

Example Question #4 : How To Find An Angle In A Parallelogram

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

Example Question #21 : Parallelograms

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

All Intermediate Geometry Resources

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