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Intermediate Geometry : How to find an angle in a trapezoid

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Example Questions

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

In the trapezoid below, find the degree measure of $\displaystyle j$ .

Possible Answers:

$76^\circ$ $\displaystyle 76^\circ$

$153^\circ$ $\displaystyle 153^\circ$

$93^\circ$ $\displaystyle 93^\circ$

$86^\circ$ $\displaystyle 86^\circ$

Correct answer:

$76^\circ$ $\displaystyle 76^\circ$

Explanation:

In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 180 $\displaystyle 180$ degrees.

$\displaystyle j$ and the angle measuring 104 $\displaystyle 104$ degrees are adjacent angles that are supplementary.

$\displaystyle j+104=180$

j=76 $\displaystyle j=76$

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

In the trapezoid below, find the angle measurement of $\displaystyle h$ .

Possible Answers:

$85^\circ$ $\displaystyle 85^\circ$

$39^\circ$ $\displaystyle 39^\circ$

$104^\circ$ $\displaystyle 104^\circ$

$153^\circ$ $\displaystyle 153^\circ$

Correct answer:

$153^\circ$ $\displaystyle 153^\circ$

Explanation:

In a trapezoid, all the interior angles add up to 360 $\displaystyle 360$ degrees.

$\displaystyle 95+85+27+h=360$

$\displaystyle 207+h=360$

h=153 $\displaystyle h=153$

$\displaystyle h$ is 153 $\displaystyle 153$ degrees.

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Example Question #11 : Trapezoids

In the trapezoid below, find the angle measurement of $\displaystyle g$ .

Possible Answers:

$143^\circ$ $\displaystyle 143^\circ$

$123^\circ$ $\displaystyle 123^\circ$

$153^\circ$ $\displaystyle 153^\circ$

$133^\circ$ $\displaystyle 133^\circ$

Correct answer:

$143^\circ$ $\displaystyle 143^\circ$

Explanation:

All the interior angles in a trapezoid add up to 360 $\displaystyle 360$ .

$\displaystyle 55+125+37+g=360$

$\displaystyle 217+g=360$

g=143 $\displaystyle g=143$

$\displaystyle g$ is 143 $\displaystyle 143$ degrees.

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

In the trapezoid below, find the angle measurement of $\displaystyle f$ .

Possible Answers:

$155^\circ$ $\displaystyle 155^\circ$

$145^\circ$ $\displaystyle 145^\circ$

$135^\circ$ $\displaystyle 135^\circ$

$165^\circ$ $\displaystyle 165^\circ$

Correct answer:

$155^\circ$ $\displaystyle 155^\circ$

Explanation:

All the interior angles in a trapezoid add up to 360 $\displaystyle 360$ .

$\displaystyle 135+45+25+f=360$

$\displaystyle 205+f=360$

f=155 $\displaystyle f=155$

$\displaystyle f$ is 155 $\displaystyle 155$ degrees.

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

In the trapezoid below, find the degree measurement of $\displaystyle e$ .

Possible Answers:

$54^\circ$ $\displaystyle 54^\circ$

$74^\circ$ $\displaystyle 74^\circ$

$64^\circ$ $\displaystyle 64^\circ$

Cannot be determined from the given information.

Correct answer:

$74^\circ$ $\displaystyle 74^\circ$

Explanation:

In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 180 $\displaystyle 180$ degrees.

$\displaystyle e$ and the angle measuring 106 $\displaystyle 106$ degrees are adjacent angles that are supplementary.

$\displaystyle e+106=180$

e=74 $\displaystyle e=74$

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

In the trapezoid below, find the degree measurement of $\displaystyle d$ .

Possible Answers:

Cannot be determined from the information given.

$102^\circ$ $\displaystyle 102^\circ$

$82^\circ$ $\displaystyle 82^\circ$

$92^\circ$ $\displaystyle 92^\circ$

Correct answer:

$102^\circ$ $\displaystyle 102^\circ$

Explanation:

In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 180 $\displaystyle 180$ degrees.

$\displaystyle d$ and the angle measuring $\displaystyle 78$ degrees are adjacent angles that are supplementary.

$\displaystyle d+78=180$

d=102 $\displaystyle d=102$

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

In the trapezoid below, find the degree measurement of $\displaystyle c$ .

Possible Answers:

$96^\circ$ $\displaystyle 96^\circ$

$86^\circ$ $\displaystyle 86^\circ$

$106^\circ$ $\displaystyle 106^\circ$

$116^\circ$ $\displaystyle 116^\circ$

Correct answer:

$116^\circ$ $\displaystyle 116^\circ$

Explanation:

In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 180 $\displaystyle 180$ degrees.

$\displaystyle c$ and the angle measuring $\displaystyle 64$ degrees are adjacent angles that are supplementary.

$\displaystyle c+64=180$

c=116 $\displaystyle c=116$

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

In the trapezoid below, find the degree measurement of $\displaystyle b$ .

Possible Answers:

$93^\circ$ $\displaystyle 93^\circ$

$73^\circ$ $\displaystyle 73^\circ$

$83^\circ$ $\displaystyle 83^\circ$

$103^\circ$ $\displaystyle 103^\circ$

Correct answer:

$93^\circ$ $\displaystyle 93^\circ$

Explanation:

In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 180 $\displaystyle 180$ degrees.

$\displaystyle b$ and the angle measuring $\displaystyle 87$ degrees are adjacent angles that are supplementary.

$\displaystyle b+87=180$

b=93 $\displaystyle b=93$

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Example Question #5 : How To Find An Angle In A Trapezoid

In the trapezoid below, find the degree measurement of $\displaystyle a$ .

Possible Answers:

$95^\circ$ $\displaystyle 95^\circ$

$105^\circ$ $\displaystyle 105^\circ$

$115^\circ$ $\displaystyle 115^\circ$

$85^\circ$ $\displaystyle 85^\circ$

Correct answer:

$105^\circ$ $\displaystyle 105^\circ$

Explanation:

In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 180 $\displaystyle 180$ degrees.

$\displaystyle a$ and the angle measuring $\displaystyle 75$ degrees are adjacent angles that are supplementary.

Therefore, we can write the following equation and solve for a.

$\displaystyle a+75=180$

a=105 $\displaystyle a=105$

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

In the trapezoid below, find the degree measurement of $\displaystyle z$ .

Possible Answers:

$65^\circ$ $\displaystyle 65^\circ$

$75^\circ$ $\displaystyle 75^\circ$

$105^\circ$ $\displaystyle 105^\circ$

$85^\circ$ $\displaystyle 85^\circ$

Correct answer:

$85^\circ$ $\displaystyle 85^\circ$

Explanation:

In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 180 $\displaystyle 180$ degrees.

$\displaystyle z$ and the angle measuring $\displaystyle 95$ degrees are adjacent angles that are supplementary.

Therefore, we can write the following equation and solve for z.

$\displaystyle z+95=180$

z=85 $\displaystyle z=85$

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Intermediate Geometry : How to find an angle in a trapezoid

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

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

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

Example Question #11 : Trapezoids

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

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

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

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

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

Example Question #5 : How To Find An Angle In A Trapezoid

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

All Intermediate Geometry Resources

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