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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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Example Questions

Example Question #59 : Geometry

The figure represents a set of supplementary angles, solve for $\displaystyle x$ .

Possible Answers:

$9^\circ$ $\displaystyle 9^\circ$

$7^\circ$ $\displaystyle 7^\circ$

$5^\circ$ $\displaystyle 5^\circ$

$6^\circ$ $\displaystyle 6^\circ$

$8^\circ$ $\displaystyle 8^\circ$

Correct answer:

$6^\circ$ $\displaystyle 6^\circ$

Explanation:

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

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

$\displaystyle x+174=180$

Next we can solve for $\displaystyle x$ :

$\frac{\begin{array}[b]{r}x+174=180\\ -174-174\end{array}}{x= 6}$ $\displaystyle \frac{\begin{array}[b]{r}x+174=180\\ -174-174\end{array}}{x= 6}$

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Example Question #31 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

Solve for $\displaystyle x$ :

Possible Answers:

$94^\circ$ $\displaystyle 94^\circ$

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

$90^\circ$ $\displaystyle 90^\circ$

$114^\circ$ $\displaystyle 114^\circ$

$87^\circ$ $\displaystyle 87^\circ$

Correct answer:

$94^\circ$ $\displaystyle 94^\circ$

Explanation:

A pair of intersecting angles is illustrated by the provided image.

$94^\circ$ $\displaystyle 94^\circ$ and $\displaystyle x$ are vertical angles because they share the same vertex, or corner spot. Vertical angles are always equal; thus, $x=94^\circ$ $\displaystyle x=94^\circ$

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Example Question #31 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

Solve for $\displaystyle x$ :

Possible Answers:

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

$162^\circ$ $\displaystyle 162^\circ$

$91^\circ$ $\displaystyle 91^\circ$

$90^\circ$ $\displaystyle 90^\circ$

$180^\circ$ $\displaystyle 180^\circ$

Correct answer:

$90^\circ$ $\displaystyle 90^\circ$

Explanation:

A pair of intersecting angles is illustrated by the provided image.

$90^\circ$ $\displaystyle 90^\circ$ and $\displaystyle x$ are vertical angles because they share the same vertex, or corner spot. Vertical angles are always equal; thus, $x=90^\circ$ $\displaystyle x=90^\circ$

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Example Question #61 : Geometry

Solve for $\displaystyle x$ :

Possible Answers:

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

$24^\circ$ $\displaystyle 24^\circ$

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

$12^\circ$ $\displaystyle 12^\circ$

$78^\circ$ $\displaystyle 78^\circ$

Correct answer:

$78^\circ$ $\displaystyle 78^\circ$

Explanation:

A pair of intersecting angles is illustrated by the provided image.

$78^\circ$ $\displaystyle 78^\circ$ and $\displaystyle x$ are vertical angles because they share the same vertex, or corner spot. Vertical angles are always equal; thus, $x=78^\circ$ $\displaystyle x=78^\circ$

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Example Question #32 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

Solve for $\displaystyle x$ :

Possible Answers:

$61^\circ$ $\displaystyle 61^\circ$

$29^\circ$ $\displaystyle 29^\circ$

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

$119^\circ$ $\displaystyle 119^\circ$

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

Correct answer:

$61^\circ$ $\displaystyle 61^\circ$

Explanation:

A pair of intersecting angles is illustrated by the provided image.

$61^\circ$ $\displaystyle 61^\circ$ and $\displaystyle x$ are vertical angles because they share the same vertex, or corner spot. Vertical angles are always equal; thus, $x=61^\circ$ $\displaystyle x=61^\circ$

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Example Question #695 : Grade 7

Solve for $\displaystyle x$ :

Possible Answers:

$40^\circ$ $\displaystyle 40^\circ$

$67^\circ$ $\displaystyle 67^\circ$

$140^\circ$ $\displaystyle 140^\circ$

$124^\circ$ $\displaystyle 124^\circ$

$50^\circ$ $\displaystyle 50^\circ$

Correct answer:

$40^\circ$ $\displaystyle 40^\circ$

Explanation:

A pair of intersecting angles is illustrated by the provided image.

$40^\circ$ $\displaystyle 40^\circ$ and $\displaystyle x$ are vertical angles because they share the same vertex, or corner spot. Vertical angles are always equal; thus, $x=40^\circ$ $\displaystyle x=40^\circ$

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Example Question #696 : Grade 7

Solve for $\displaystyle x$ :

Possible Answers:

$22^\circ$ $\displaystyle 22^\circ$

$169^\circ$ $\displaystyle 169^\circ$

$11^\circ$ $\displaystyle 11^\circ$

$79^\circ$ $\displaystyle 79^\circ$

$19^\circ$ $\displaystyle 19^\circ$

Correct answer:

$11^\circ$ $\displaystyle 11^\circ$

Explanation:

A pair of intersecting angles is illustrated by the provided image.

$11^\circ$ $\displaystyle 11^\circ$ and $\displaystyle x$ are vertical angles because they share the same vertex, or corner spot. Vertical angles are always equal; thus, $x=11^\circ$ $\displaystyle x=11^\circ$

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Example Question #31 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

Solve for $\displaystyle x$ :

Possible Answers:

$122^\circ$ $\displaystyle 122^\circ$

$11^\circ$ $\displaystyle 11^\circ$

$111^\circ$ $\displaystyle 111^\circ$

$169^\circ$ $\displaystyle 169^\circ$

$121^\circ$ $\displaystyle 121^\circ$

Correct answer:

$169^\circ$ $\displaystyle 169^\circ$

Explanation:

A pair of intersecting angles is illustrated by the provided image.

$169^\circ$ $\displaystyle 169^\circ$ and $\displaystyle x$ are vertical angles because they share the same vertex, or corner spot. Vertical angles are always equal; thus, $x=169^\circ$ $\displaystyle x=169^\circ$

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Example Question #31 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

Solve for $\displaystyle x$ :

Possible Answers:

$62^\circ$ $\displaystyle 62^\circ$

$28^\circ$ $\displaystyle 28^\circ$

$78^\circ$ $\displaystyle 78^\circ$

$80^\circ$ $\displaystyle 80^\circ$

$152^\circ$ $\displaystyle 152^\circ$

Correct answer:

$152^\circ$ $\displaystyle 152^\circ$

Explanation:

A pair of intersecting angles is illustrated by the provided image.

$152^\circ$ $\displaystyle 152^\circ$ and $\displaystyle x$ are vertical angles because they share the same vertex, or corner spot. Vertical angles are always equal; thus, $x=152^\circ$ $\displaystyle x=152^\circ$

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Example Question #61 : Geometry

Solve for $\displaystyle x$ :

Possible Answers:

$98^\circ$ $\displaystyle 98^\circ$

$156^\circ$ $\displaystyle 156^\circ$

$147^\circ$ $\displaystyle 147^\circ$

$66^\circ$ $\displaystyle 66^\circ$

$33^\circ$ $\displaystyle 33^\circ$

Correct answer:

$147^\circ$ $\displaystyle 147^\circ$

Explanation:

A pair of intersecting angles is illustrated by the provided image.

$147^\circ$ $\displaystyle 147^\circ$ and $\displaystyle x$ are vertical angles because they share the same vertex, or corner spot. Vertical angles are always equal; thus, $x=147^\circ$ $\displaystyle x=147^\circ$

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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 #59 : Geometry

Example Question #31 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

Example Question #31 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

Example Question #61 : Geometry

Example Question #32 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

Example Question #695 : Grade 7

Example Question #696 : Grade 7

Example Question #31 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

Example Question #31 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

Example Question #61 : Geometry

All Common Core: 7th Grade Math Resources

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