Establish Angle Facts Using Arguments - 8th Grade Math
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When two parallel lines are cut by a transversal, what is true about same-side (consecutive) interior angles?
When two parallel lines are cut by a transversal, what is true about same-side (consecutive) interior angles?
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They are supplementary: sum is $180^\circ$. They're on the same side of the transversal between parallels.
They are supplementary: sum is $180^\circ$. They're on the same side of the transversal between parallels.
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Find $x$ if alternate interior angles are $5x-15$ and $3x+25$ degrees for parallel lines.
Find $x$ if alternate interior angles are $5x-15$ and $3x+25$ degrees for parallel lines.
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$x=20$. Alternate interior angles are equal: $5x - 15 = 3x + 25$.
$x=20$. Alternate interior angles are equal: $5x - 15 = 3x + 25$.
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Find the third angle of a triangle if two angles are $x^\circ$ and $x^\circ$ and the third is $40^\circ$; find $x$.
Find the third angle of a triangle if two angles are $x^\circ$ and $x^\circ$ and the third is $40^\circ$; find $x$.
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$x=70^\circ$. $x + x + 40 = 180°$, so $2x = 140°$.
$x=70^\circ$. $x + x + 40 = 180°$, so $2x = 140°$.
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Identify whether triangles are similar by AA if one has angles $40^\circ$ and $70^\circ$ and the other has $40^\circ$ and $70^\circ$.
Identify whether triangles are similar by AA if one has angles $40^\circ$ and $70^\circ$ and the other has $40^\circ$ and $70^\circ$.
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Yes, they are similar by $AA$. Two pairs of equal angles satisfy the AA criterion.
Yes, they are similar by $AA$. Two pairs of equal angles satisfy the AA criterion.
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Find $x$ if same-side interior angles are $2x+20$ and $3x+10$ degrees for parallel lines.
Find $x$ if same-side interior angles are $2x+20$ and $3x+10$ degrees for parallel lines.
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$x=30$. Same-side angles sum to $180°$: $(2x + 20) + (3x + 10) = 180°$.
$x=30$. Same-side angles sum to $180°$: $(2x + 20) + (3x + 10) = 180°$.
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Find $x$ if corresponding angles formed by a transversal are labeled $3x+10$ and $7x-30$ degrees.
Find $x$ if corresponding angles formed by a transversal are labeled $3x+10$ and $7x-30$ degrees.
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$x=10$. Corresponding angles are equal: $3x + 10 = 7x - 30$.
$x=10$. Corresponding angles are equal: $3x + 10 = 7x - 30$.
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Find $x$ if an exterior angle is $140^\circ$ and its adjacent interior angle is $x^\circ$.
Find $x$ if an exterior angle is $140^\circ$ and its adjacent interior angle is $x^\circ$.
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$x=40^\circ$. $140° + x = 180°$ since they're supplementary.
$x=40^\circ$. $140° + x = 180°$ since they're supplementary.
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Find the exterior angle measure if the two remote interior angles are $35^\circ$ and $75^\circ$.
Find the exterior angle measure if the two remote interior angles are $35^\circ$ and $75^\circ$.
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$110^\circ$. Exterior angle equals the sum of remote interior angles.
$110^\circ$. Exterior angle equals the sum of remote interior angles.
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Find $x$ if an exterior angle of a triangle is $110^\circ$ and one remote interior angle is $45^\circ$.
Find $x$ if an exterior angle of a triangle is $110^\circ$ and one remote interior angle is $45^\circ$.
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$x=65^\circ$. $110° = 45° + x$, so $x = 110° - 45°$.
$x=65^\circ$. $110° = 45° + x$, so $x = 110° - 45°$.
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Find $x$ if the interior angles of a triangle are $50^\circ$, $60^\circ$, and $x^\circ$.
Find $x$ if the interior angles of a triangle are $50^\circ$, $60^\circ$, and $x^\circ$.
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$x=70^\circ$. $50° + 60° + x = 180°$, so $x = 180° - 110°$.
$x=70^\circ$. $50° + 60° + x = 180°$, so $x = 180° - 110°$.
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What is always true about a linear pair of angles?
What is always true about a linear pair of angles?
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They are supplementary: sum is $180^\circ$. Adjacent angles that form a straight line.
They are supplementary: sum is $180^\circ$. Adjacent angles that form a straight line.
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What is always true about vertical angles formed by two intersecting lines?
What is always true about vertical angles formed by two intersecting lines?
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Vertical angles are congruent. Opposite angles formed by intersecting lines are always equal.
Vertical angles are congruent. Opposite angles formed by intersecting lines are always equal.
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When two parallel lines are cut by a transversal, which angle pair is always congruent: alternate interior angles or same-side interior angles?
When two parallel lines are cut by a transversal, which angle pair is always congruent: alternate interior angles or same-side interior angles?
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Alternate interior angles are congruent. They form a Z-pattern and are equal when lines are parallel.
Alternate interior angles are congruent. They form a Z-pattern and are equal when lines are parallel.
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When two parallel lines are cut by a transversal, which angle pair is always congruent: corresponding angles or adjacent angles?
When two parallel lines are cut by a transversal, which angle pair is always congruent: corresponding angles or adjacent angles?
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Corresponding angles are congruent. They occupy the same position relative to the transversal.
Corresponding angles are congruent. They occupy the same position relative to the transversal.
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What is the angle-angle similarity criterion for triangles?
What is the angle-angle similarity criterion for triangles?
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If two angles are congruent, the triangles are similar. Two pairs of equal angles guarantee the third pair is also equal.
If two angles are congruent, the triangles are similar. Two pairs of equal angles guarantee the third pair is also equal.
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What is the measure of each exterior angle of an equilateral triangle?
What is the measure of each exterior angle of an equilateral triangle?
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Each exterior angle is $120^\circ$. Each supplements its adjacent $60°$ interior angle.
Each exterior angle is $120^\circ$. Each supplements its adjacent $60°$ interior angle.
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What is the measure of each interior angle in an equilateral triangle?
What is the measure of each interior angle in an equilateral triangle?
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Each interior angle is $60^\circ$. All three equal angles must sum to $180°$, so each is $180° ÷ 3$.
Each interior angle is $60^\circ$. All three equal angles must sum to $180°$, so each is $180° ÷ 3$.
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Identify the relationship between an exterior angle and its adjacent interior angle in a triangle.
Identify the relationship between an exterior angle and its adjacent interior angle in a triangle.
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They are supplementary: sum is $180^\circ$. They form a straight angle on the same line.
They are supplementary: sum is $180^\circ$. They form a straight angle on the same line.
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What is the exterior angle of a triangle equal to in terms of the two remote interior angles?
What is the exterior angle of a triangle equal to in terms of the two remote interior angles?
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Exterior angle $=$ sum of the two remote interior angles. Forms a straight line with the adjacent interior angle.
Exterior angle $=$ sum of the two remote interior angles. Forms a straight line with the adjacent interior angle.
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What is the sum of the interior angles of any triangle?
What is the sum of the interior angles of any triangle?
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$180^\circ$. The three angles of any triangle always add up to a straight angle.
$180^\circ$. The three angles of any triangle always add up to a straight angle.
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Find the adjacent interior angle if an exterior angle of a triangle is $118^\circ$.
Find the adjacent interior angle if an exterior angle of a triangle is $118^\circ$.
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$62^\circ$. $180^\circ - 118^\circ = 62^\circ$ since they form a linear pair.
$62^\circ$. $180^\circ - 118^\circ = 62^\circ$ since they form a linear pair.
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Find the exterior angle of a triangle if the two remote interior angles are $50^\circ$ and $60^\circ$.
Find the exterior angle of a triangle if the two remote interior angles are $50^\circ$ and $60^\circ$.
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$110^\circ$. $50^\circ + 60^\circ = 110^\circ$ using the exterior angle theorem.
$110^\circ$. $50^\circ + 60^\circ = 110^\circ$ using the exterior angle theorem.
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Identify whether triangles are similar by AA: Triangle $1$ has angles $40^\circ,70^\circ$; Triangle $2$ has $40^\circ,70^\circ$.
Identify whether triangles are similar by AA: Triangle $1$ has angles $40^\circ,70^\circ$; Triangle $2$ has $40^\circ,70^\circ$.
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Yes, similar by $AA$. Two pairs of congruent angles satisfy the AA criterion.
Yes, similar by $AA$. Two pairs of congruent angles satisfy the AA criterion.
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Find the missing angle in Triangle $2$ if Triangle $1$ is similar by $AA$ with angles $35^\circ,65^\circ$ and Triangle $2$ has $35^\circ$ and $x$.
Find the missing angle in Triangle $2$ if Triangle $1$ is similar by $AA$ with angles $35^\circ,65^\circ$ and Triangle $2$ has $35^\circ$ and $x$.
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$x=65^\circ$. Similar triangles have all corresponding angles congruent.
$x=65^\circ$. Similar triangles have all corresponding angles congruent.
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Two lines are parallel. If a same-side interior angle is $112^\circ$, what is the other same-side interior angle?
Two lines are parallel. If a same-side interior angle is $112^\circ$, what is the other same-side interior angle?
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$68^\circ$. $180^\circ - 112^\circ = 68^\circ$ since they're supplementary.
$68^\circ$. $180^\circ - 112^\circ = 68^\circ$ since they're supplementary.
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Two lines are parallel. If an alternate interior angle is $105^\circ$, what is its alternate interior partner?
Two lines are parallel. If an alternate interior angle is $105^\circ$, what is its alternate interior partner?
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$105^\circ$. Alternate interior angles are congruent when lines are parallel.
$105^\circ$. Alternate interior angles are congruent when lines are parallel.
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Two lines are parallel. If a corresponding angle is $72^\circ$, what is the measure of its corresponding partner?
Two lines are parallel. If a corresponding angle is $72^\circ$, what is the measure of its corresponding partner?
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$72^\circ$. Corresponding angles are congruent when lines are parallel.
$72^\circ$. Corresponding angles are congruent when lines are parallel.
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Find the measure of each angle in an equilateral triangle.
Find the measure of each angle in an equilateral triangle.
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Each angle is $60^\circ$. $180^\circ \div 3 = 60^\circ$ since all angles are equal.
Each angle is $60^\circ$. $180^\circ \div 3 = 60^\circ$ since all angles are equal.
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Find the third angle of a triangle if two angles are $65^\circ$ and $45^\circ$.
Find the third angle of a triangle if two angles are $65^\circ$ and $45^\circ$.
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$70^\circ$. $180^\circ - 65^\circ - 45^\circ = 70^\circ$ using the triangle angle sum.
$70^\circ$. $180^\circ - 65^\circ - 45^\circ = 70^\circ$ using the triangle angle sum.
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Find the remote interior angle if an exterior angle is $130^\circ$ and the other remote interior angle is $55^\circ$.
Find the remote interior angle if an exterior angle is $130^\circ$ and the other remote interior angle is $55^\circ$.
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$75^\circ$. $130^\circ - 55^\circ = 75^\circ$ using the exterior angle theorem.
$75^\circ$. $130^\circ - 55^\circ = 75^\circ$ using the exterior angle theorem.
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