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Common Core: 7th Grade Math : Solve Simple Equations for an Unknown Angle in a Figure: CCSS.Math.Content.7.G.B.5

Study concepts, example questions & explanations for Common Core: 7th Grade Math

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All Common Core: 7th Grade Math Resources

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Example Questions

Example Question #33 : Geometry

The figure represents a set of complementary angles, solve for .

Possible Answers:

$77^\circ$

$76^\circ$

$78^\circ$

$80^\circ$

$79^\circ$

Correct answer:

$78^\circ$

Explanation:

Complementary angles are defined as two angles that when added together equal $90^\circ$

From the question, we know that the two angles are complimentary, and thus equal $90^\circ$ , so we can set up the following equation:

x+12=90

Next we can solve for :

$\frac{\begin{array}[b]{r}x+12=90\\ -12-12\end{array}}{x= 78}$

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Example Question #41 : Geometry

The figure represents a set of complementary angles, solve for .

Possible Answers:

$45^\circ$

$49^\circ$

$48^\circ$

$46^\circ$

$47^\circ$

Correct answer:

$45^\circ$

Explanation:

Complementary angles are defined as two angles that when added together equal $90^\circ$

From the question, we know that the two angles are complimentary, and thus equal $90^\circ$ , so we can set up the following equation:

x+45=90

Next we can solve for :

$\frac{\begin{array}[b]{r}x+45=90\\ -45-45\end{array}}{x= 45}$

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Example Question #42 : Geometry

The figure represents a set of complementary angles, solve for .

Possible Answers:

$81^\circ$

$84^\circ$

$85^\circ$

$82^\circ$

$83^\circ$

Correct answer:

$85^\circ$

Explanation:

Complementary angles are defined as two angles that when added together equal $90^\circ$

From the question, we know that the two angles are complimentary, and thus equal $90^\circ$ , so we can set up the following equation:

x+5=90

Next we can solve for :

$\frac{\begin{array}[b]{r}x+5=90\\ -5-5\end{array}}{x= 85}$

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Example Question #43 : Geometry

The figure represents a set of complementary angles, solve for .

Possible Answers:

$39^\circ$

$41^\circ$

$38^\circ$

$40^\circ$

$42^\circ$

Correct answer:

$38^\circ$

Explanation:

Complementary angles are defined as two angles that when added together equal $90^\circ$

From the question, we know that the two angles are complimentary, and thus equal $90^\circ$ , so we can set up the following equation:

x+52=90

Next we can solve for :

$\frac{\begin{array}[b]{r}x+52=90\\ -52-52\end{array}}{x= 38}$

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Example Question #44 : Geometry

The figure represents a set of complementary angles, solve for .

Possible Answers:

$29^\circ$

$30^\circ$

$27^\circ$

$26^\circ$

$28^\circ$

Correct answer:

$29^\circ$

Explanation:

Complementary angles are defined as two angles that when added together equal $90^\circ$

From the question, we know that the two angles are complimentary, and thus equal $90^\circ$ , so we can set up the following equation:

x+61=90

Next we can solve for :

$\frac{\begin{array}[b]{r}x+61=90\\ -61-61\end{array}}{x= 29}$

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Example Question #45 : Geometry

The figure represents a set of complementary angles, solve for .

Possible Answers:

$22^\circ$

$23^\circ$

$26^\circ$

$24^\circ$

$25^\circ$

Correct answer:

$23^\circ$

Explanation:

Complementary angles are defined as two angles that when added together equal $90^\circ$

From the question, we know that the two angles are complimentary, and thus equal $90^\circ$ , so we can set up the following equation:

x+67=90

Next we can solve for :

$\frac{\begin{array}[b]{r}x+67=90\\ -67-67\end{array}}{x= 23}$

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Example Question #46 : Geometry

The figure represents a set of complementary angles, solve for .

Possible Answers:

$16^\circ$

$12^\circ$

$14^\circ$

$13^\circ$

$15^\circ$

Correct answer:

$14^\circ$

Explanation:

Complementary angles are defined as two angles that when added together equal $90^\circ$

From the question, we know that the two angles are complimentary, and thus equal $90^\circ$ , so we can set up the following equation:

x+76=90

Next we can solve for :

$\frac{\begin{array}[b]{r}x+76=90\\ -76-76\end{array}}{x= 14}$

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Example Question #47 : Geometry

The figure represents a set of complementary angles, solve for .

Possible Answers:

$13^\circ$

$14^\circ$

$11^\circ$

$10^\circ$

$12^\circ$

Correct answer:

$10^\circ$

Explanation:

Complementary angles are defined as two angles that when added together equal $90^\circ$

From the question, we know that the two angles are complimentary, and thus equal $90^\circ$ , so we can set up the following equation:

x+80=90

Next we can solve for :

$\frac{\begin{array}[b]{r}x+80=90\\ -80-80\end{array}}{x= 10}$

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Example Question #48 : Geometry

The figure represents a set of complementary angles, solve for .

Possible Answers:

$7^\circ$

$5^\circ$

$9^\circ$

$8^\circ$

$6^\circ$

Correct answer:

$6^\circ$

Explanation:

Complementary angles are defined as two angles that when added together equal $90^\circ$

From the question, we know that the two angles are complimentary, and thus equal $90^\circ$ , so we can set up the following equation:

x+84=90

Next we can solve for :

$\frac{\begin{array}[b]{r}x+84=90\\ -84-84\end{array}}{x= 6}$

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Example Question #49 : Geometry

The figure represents a set of supplementary angles, solve for .

Possible Answers:

$93^\circ$

$90^\circ$

$92^\circ$

$91^\circ$

$94^\circ$

Correct answer:

$90^\circ$

Explanation:

Supplementary angles are defined as two angles that when added together equal $180^\circ$

From the question, we know that the two angles are supplementary, and thus equal $180^\circ$ , so we can set up the following equation:

x+90=180

Next we can solve for :

$\frac{\begin{array}[b]{r}x+90=180\\ -90-90\end{array}}{x= 90}$

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Common Core: 7th Grade Math : Solve Simple Equations for an Unknown Angle in a Figure: CCSS.Math.Content.7.G.B.5

Study concepts, example questions & explanations for Common Core: 7th Grade Math

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #33 : Geometry

Example Question #41 : Geometry

Example Question #42 : Geometry

Example Question #43 : Geometry

Example Question #44 : Geometry

Example Question #45 : Geometry

Example Question #46 : Geometry

Example Question #47 : Geometry

Example Question #48 : Geometry

Example Question #49 : Geometry

All Common Core: 7th Grade Math Resources

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