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ISEE Upper Level Math : How to find an angle in other quadrilaterals

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Example Questions

Example Question #1 : Quadrilaterals

Three of the interior angles of a quadrilateral measure $51^{\circ }$ $\displaystyle 51^{\circ }$, $120 ^{\circ }$ $\displaystyle 120 ^{\circ }$, and $77^{\circ}$ $\displaystyle 77^{\circ}$. What is the measure of the fourth interior angle?

Possible Answers:

$102^{\circ }$ $\displaystyle 102^{\circ }$

$112^{\circ }$ $\displaystyle 112^{\circ }$

$122^{\circ }$ $\displaystyle 122^{\circ }$

This quadrilateral cannot exist.

$92^{\circ }$ $\displaystyle 92^{\circ }$

Correct answer:

$112^{\circ }$ $\displaystyle 112^{\circ }$

Explanation:

The measures of the angles of a quadrilateral have sum $360^{\circ }$ $\displaystyle 360^{\circ }$. If $\displaystyle x$ is the measure of the unknown angle, then:

$\displaystyle x + 51 + 120 + 77 = 360$

$\displaystyle x + 248 = 360$

$\displaystyle x + 248 -248 = 360-248$

x = 112 $\displaystyle x = 112$

The angle measures $112^{\circ }$ $\displaystyle 112^{\circ }$.

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Example Question #1 : How To Find An Angle In Other Quadrilaterals

The angles of a quadrilateral measure $x^{\circ }, x^{\circ }, \left ( x+45 \right ) ^{\circ }, \left ( x+65 \right ) ^{\circ }$ $\displaystyle x^{\circ }, x^{\circ }, \left ( x+45 \right ) ^{\circ }, \left ( x+65 \right ) ^{\circ }$. Evaluate $\displaystyle x$.

Possible Answers:

x = 70 $\displaystyle x = 70$

$\displaystyle x = 62.5$

$\displaystyle x = 67.5$

x = 65 $\displaystyle x = 65$

Correct answer:

$\displaystyle x = 62.5$

Explanation:

The sum of the degree measures of the angles of a quadrilateral is 360, so we can set up and solve for $\displaystyle x$ in the equation:

$x + x + \left ( x+45 \right ) + \left ( x+65 \right ) = 360$ $\displaystyle x + x + \left ( x+45 \right ) + \left ( x+65 \right ) = 360$

$\displaystyle 4x+110= 360$

$\displaystyle 4x+110- 110 = 360 - 110$

$\displaystyle 4x = 250$

$4x\div 4 = 250 \div 4$ $\displaystyle 4x\div 4 = 250 \div 4$

$\displaystyle x = 62.5$

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Example Question #1 : Quadrilaterals

The four angles of a quadrilateral have the following value: 79 degrees, 100 degrees, 50 degrees, and $\displaystyle 2x$ degrees. What is the value of $\displaystyle x$?

Possible Answers:

65.5 $\displaystyle 65.5$

131 $\displaystyle 131$

130 $\displaystyle 130$

$\displaystyle 65$

Correct answer:

65.5 $\displaystyle 65.5$

Explanation:

Given that there are 360 degrees when all the angles of a quadrilateral are added toghether, this problem can be solved with the following equation:

$\displaystyle 360 = 79 +100 +50 + 2x$

$\displaystyle 360=229+2x$

131=2x $\displaystyle 131=2x$

x=65.5 $\displaystyle x=65.5$

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Example Question #231 : Plane Geometry

In a quadrilateral, the angles have the following values:

$94^{\circ},27^{\circ},81^{\circ},\textup{and }(4x)^{\circ}$ $\displaystyle 94^{\circ},27^{\circ},81^{\circ},\textup{and }(4x)^{\circ}$.

What is the value of $\displaystyle x$?

Possible Answers:

$\displaystyle 40$

$\displaystyle 51$

39.5 $\displaystyle 39.5$

158 $\displaystyle 158$

Correct answer:

39.5 $\displaystyle 39.5$

Explanation:

Given that there are 360 degrees when the angles of a quadrilateral are added together, it follows that:

$\displaystyle 94 + 27+ 81 + 4x =360$

$\displaystyle 202+4x=360$

4x=158 $\displaystyle 4x=158$

x=39.5 $\displaystyle x=39.5$

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : How to find an angle in other quadrilaterals

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : Quadrilaterals

Example Question #1 : How To Find An Angle In Other Quadrilaterals

Example Question #1 : Quadrilaterals

Example Question #231 : Plane Geometry

All ISEE Upper Level Math Resources

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