Solve Problems With Angle Relationships - 7th Grade Math
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What is $x$ if a linear pair has measures $(2x+10)^\circ$ and $90^\circ$?
What is $x$ if a linear pair has measures $(2x+10)^\circ$ and $90^\circ$?
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$x=40$. Since $(2x + 10) + 90 = 180$, solve: $2x = 80$, so $x = 40$.
$x=40$. Since $(2x + 10) + 90 = 180$, solve: $2x = 80$, so $x = 40$.
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What is the missing angle if one angle in a supplementary pair is $147^\circ$?
What is the missing angle if one angle in a supplementary pair is $147^\circ$?
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$33^\circ$. Subtract from $180^\circ$: $180 - 147 = 33$.
$33^\circ$. Subtract from $180^\circ$: $180 - 147 = 33$.
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What is $x$ if vertical angles measure $(5x-10)^\circ$ and $(3x+30)^\circ$?
What is $x$ if vertical angles measure $(5x-10)^\circ$ and $(3x+30)^\circ$?
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$x=20$. Set $5x - 10 = 3x + 30$, then $2x = 40$, so $x = 20$.
$x=20$. Set $5x - 10 = 3x + 30$, then $2x = 40$, so $x = 20$.
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What is $x$ if supplementary angles measure $(x+15)^\circ$ and $(2x+45)^\circ$?
What is $x$ if supplementary angles measure $(x+15)^\circ$ and $(2x+45)^\circ$?
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$x=40$. Set $(x + 15) + (2x + 45) = 180$, then $3x + 60 = 180$.
$x=40$. Set $(x + 15) + (2x + 45) = 180$, then $3x + 60 = 180$.
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What is the definition of adjacent angles?
What is the definition of adjacent angles?
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Two angles that share a common vertex and a common side. They are next to each other with a shared ray between them.
Two angles that share a common vertex and a common side. They are next to each other with a shared ray between them.
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What is $x$ if adjacent angles add to a right angle and measure $x^\circ$ and $(x+20)^\circ$?
What is $x$ if adjacent angles add to a right angle and measure $x^\circ$ and $(x+20)^\circ$?
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$x=35$. Set $x + (x + 20) = 90$, then $2x + 20 = 90$, so $x = 35$.
$x=35$. Set $x + (x + 20) = 90$, then $2x + 20 = 90$, so $x = 35$.
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What is the definition of vertical angles formed by intersecting lines?
What is the definition of vertical angles formed by intersecting lines?
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Opposite angles formed by intersecting lines. They share a vertex but not sides when lines cross.
Opposite angles formed by intersecting lines. They share a vertex but not sides when lines cross.
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What is $x$ if vertical angles have measures $(3x+5)^\circ$ and $50^\circ$?
What is $x$ if vertical angles have measures $(3x+5)^\circ$ and $50^\circ$?
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$x=15$. Set $3x + 5 = 50$, then solve: $3x = 45$, so $x = 15$.
$x=15$. Set $3x + 5 = 50$, then solve: $3x = 45$, so $x = 15$.
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What is $x$ if two supplementary angles have measures $x^\circ$ and $128^\circ$?
What is $x$ if two supplementary angles have measures $x^\circ$ and $128^\circ$?
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$x=52$. Since $x + 128 = 180$, subtract 128 from both sides.
$x=52$. Since $x + 128 = 180$, subtract 128 from both sides.
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What is $x$ if two complementary angles have measures $x^\circ$ and $35^\circ$?
What is $x$ if two complementary angles have measures $x^\circ$ and $35^\circ$?
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$x=55$. Since $x + 35 = 90$, subtract 35 from both sides.
$x=55$. Since $x + 35 = 90$, subtract 35 from both sides.
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What is always true about the measures of angles in a linear pair?
What is always true about the measures of angles in a linear pair?
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They are supplementary: sum is $180^\circ$. Linear pairs always form a straight angle together.
They are supplementary: sum is $180^\circ$. Linear pairs always form a straight angle together.
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What is a linear pair of angles?
What is a linear pair of angles?
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Adjacent angles whose noncommon sides form a line. Their outer rays form a straight line ($180^\circ$).
Adjacent angles whose noncommon sides form a line. Their outer rays form a straight line ($180^\circ$).
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What is $x$ if a linear pair measures $(4x)^\circ$ and $(2x+30)^\circ$?
What is $x$ if a linear pair measures $(4x)^\circ$ and $(2x+30)^\circ$?
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$x=25$. Set $4x + (2x + 30) = 180$, then $6x + 30 = 180$.
$x=25$. Set $4x + (2x + 30) = 180$, then $6x + 30 = 180$.
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What is always true about the measures of vertical angles?
What is always true about the measures of vertical angles?
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Vertical angles are congruent (equal in measure). This property makes them useful for finding unknown angles.
Vertical angles are congruent (equal in measure). This property makes them useful for finding unknown angles.
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What is the definition of complementary angles in terms of their measures?
What is the definition of complementary angles in terms of their measures?
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Two angles whose measures sum to $90^\circ$. The sum of their measures equals a right angle.
Two angles whose measures sum to $90^\circ$. The sum of their measures equals a right angle.
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What is the definition of supplementary angles in terms of their measures?
What is the definition of supplementary angles in terms of their measures?
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Two angles whose measures sum to $180^\circ$. The sum of their measures equals a straight angle.
Two angles whose measures sum to $180^\circ$. The sum of their measures equals a straight angle.
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What is $x$ if intersecting lines create vertical angles $x^\circ$ and $x^\circ$, and an adjacent angle is $110^\circ$?
What is $x$ if intersecting lines create vertical angles $x^\circ$ and $x^\circ$, and an adjacent angle is $110^\circ$?
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$x=70$. Adjacent to vertical angles forms linear pair: $x + 110 = 180$.
$x=70$. Adjacent to vertical angles forms linear pair: $x + 110 = 180$.
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What is $x$ if a straight angle is split into three adjacent angles: $x^\circ$, $(x+20)^\circ$, and $40^\circ$?
What is $x$ if a straight angle is split into three adjacent angles: $x^\circ$, $(x+20)^\circ$, and $40^\circ$?
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$x=60$. Set $x + (x + 20) + 40 = 180$, then $2x + 60 = 180$.
$x=60$. Set $x + (x + 20) + 40 = 180$, then $2x + 60 = 180$.
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What is the missing angle if one angle in a complementary pair is $62^\circ$?
What is the missing angle if one angle in a complementary pair is $62^\circ$?
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$28^\circ$. Subtract from $90^\circ$: $90 - 62 = 28$.
$28^\circ$. Subtract from $90^\circ$: $90 - 62 = 28$.
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Find $x$: vertical angles are labeled $(5x - 20)^\circ$ and $(3x + 16)^\circ$.
Find $x$: vertical angles are labeled $(5x - 20)^\circ$ and $(3x + 16)^\circ$.
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$x = 18$. Set vertical angles equal: $5x - 20 = 3x + 16$.
$x = 18$. Set vertical angles equal: $5x - 20 = 3x + 16$.
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Find $x$: $\angle A$ and $\angle B$ are vertical; $m\angle A = (x + 7)^\circ$, $m\angle B = (2x - 13)^\circ$.
Find $x$: $\angle A$ and $\angle B$ are vertical; $m\angle A = (x + 7)^\circ$, $m\angle B = (2x - 13)^\circ$.
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$x = 20$. Set vertical angles equal: $x + 7 = 2x - 13$.
$x = 20$. Set vertical angles equal: $x + 7 = 2x - 13$.
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What is the definition of complementary angles?
What is the definition of complementary angles?
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Two angles whose measures add to $90^\circ$. Their sum equals a right angle.
Two angles whose measures add to $90^\circ$. Their sum equals a right angle.
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What is the relationship between angles that form a linear pair?
What is the relationship between angles that form a linear pair?
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They are supplementary, so their sum is $180^\circ$. Adjacent angles on a straight line form a linear pair.
They are supplementary, so their sum is $180^\circ$. Adjacent angles on a straight line form a linear pair.
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What equation represents complementary angles with measures $x^\circ$ and $y^\circ$?
What equation represents complementary angles with measures $x^\circ$ and $y^\circ$?
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$x + y = 90$. Complementary angles sum to $90^\circ$.
$x + y = 90$. Complementary angles sum to $90^\circ$.
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What equation represents supplementary angles with measures $x^\circ$ and $y^\circ$?
What equation represents supplementary angles with measures $x^\circ$ and $y^\circ$?
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$x + y = 180$. Supplementary angles sum to $180^\circ$.
$x + y = 180$. Supplementary angles sum to $180^\circ$.
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