Lines & Angles - ACT Math
Card 1 of 30
Find the measure of an angle in a regular nonagon.
Find the measure of an angle in a regular nonagon.
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$140^{\text{°}}$. Using formula: $\frac{(9-2)\times180°}{9} = 140°$.
$140^{\text{°}}$. Using formula: $\frac{(9-2)\times180°}{9} = 140°$.
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What is the definition of vertical angles?
What is the definition of vertical angles?
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Opposite angles formed by intersecting lines; they are congruent. They have equal measures when lines cross.
Opposite angles formed by intersecting lines; they are congruent. They have equal measures when lines cross.
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What is the definition of adjacent angles?
What is the definition of adjacent angles?
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Two angles sharing a vertex and a side with nonoverlapping interiors. Next to each other but don't overlap inside.
Two angles sharing a vertex and a side with nonoverlapping interiors. Next to each other but don't overlap inside.
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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 straight line ($180^\circ$). Adjacent angles that together form a line.
Adjacent angles whose noncommon sides form a straight line ($180^\circ$). Adjacent angles that together form a line.
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If two angles form a linear pair, what equation relates their measures?
If two angles form a linear pair, what equation relates their measures?
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$m\angle 1 + m\angle 2 = 180^\circ$. Linear pairs always sum to a straight angle.
$m\angle 1 + m\angle 2 = 180^\circ$. Linear pairs always sum to a straight angle.
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If two angles are supplementary, what equation relates their measures?
If two angles are supplementary, what equation relates their measures?
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$m\angle 1 + m\angle 2 = 180^\circ$. Definition of supplementary angles.
$m\angle 1 + m\angle 2 = 180^\circ$. Definition of supplementary angles.
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When a transversal cuts parallel lines, what is true about alternate interior angles?
When a transversal cuts parallel lines, what is true about alternate interior angles?
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Alternate interior angles are congruent. Interior angles on opposite sides are equal.
Alternate interior angles are congruent. Interior angles on opposite sides are equal.
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When a transversal cuts parallel lines, what is true about alternate exterior angles?
When a transversal cuts parallel lines, what is true about alternate exterior angles?
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Alternate exterior angles are congruent. Exterior angles on opposite sides are equal.
Alternate exterior angles are congruent. Exterior angles on opposite sides are equal.
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When a transversal cuts parallel lines, what is true about same-side interior angles?
When a transversal cuts parallel lines, what is true about same-side interior angles?
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Same-side interior angles are supplementary. Interior angles on same side add to $180^\circ$.
Same-side interior angles are supplementary. Interior angles on same side add to $180^\circ$.
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Which condition proves two lines are parallel using alternate interior angles?
Which condition proves two lines are parallel using alternate interior angles?
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If alternate interior angles are congruent, the lines are parallel. Converse of alternate interior angles theorem.
If alternate interior angles are congruent, the lines are parallel. Converse of alternate interior angles theorem.
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What is the exterior angle theorem for a triangle?
What is the exterior angle theorem for a triangle?
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An exterior angle equals the sum of the two remote interior angles. Exterior equals sum of non-adjacent interior angles.
An exterior angle equals the sum of the two remote interior angles. Exterior equals sum of non-adjacent interior angles.
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If two lines are perpendicular, what is the measure of the angles formed?
If two lines are perpendicular, what is the measure of the angles formed?
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All four angles measure $90^\circ$. Perpendicular lines form right angles.
All four angles measure $90^\circ$. Perpendicular lines form right angles.
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If two angles are vertical and one measures $37^\circ$, what is the other?
If two angles are vertical and one measures $37^\circ$, what is the other?
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$37^\circ$. Vertical angles are always congruent.
$37^\circ$. Vertical angles are always congruent.
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If two angles form a linear pair and one measures $112^\circ$, what is the other?
If two angles form a linear pair and one measures $112^\circ$, what is the other?
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$68^\circ$. Linear pairs sum to $180^\circ$.
$68^\circ$. Linear pairs sum to $180^\circ$.
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If two angles are complementary and one measures $29^\circ$, what is the other?
If two angles are complementary and one measures $29^\circ$, what is the other?
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$61^\circ$. Complementary angles sum to $90^\circ$.
$61^\circ$. Complementary angles sum to $90^\circ$.
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If two angles are supplementary and one measures $145^\circ$, what is the other?
If two angles are supplementary and one measures $145^\circ$, what is the other?
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$35^\circ$. Supplementary angles sum to $180^\circ$.
$35^\circ$. Supplementary angles sum to $180^\circ$.
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If corresponding angles measure $(3x+10)^\circ$ and $(5x-30)^\circ$, what is $x$?
If corresponding angles measure $(3x+10)^\circ$ and $(5x-30)^\circ$, what is $x$?
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$20$. Set corresponding angles equal and solve.
$20$. Set corresponding angles equal and solve.
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If same-side interior angles measure $(4x+10)^\circ$ and $(2x+50)^\circ$, what is $x$?
If same-side interior angles measure $(4x+10)^\circ$ and $(2x+50)^\circ$, what is $x$?
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$20$. Same-side interior angles sum to $180^\circ$.
$20$. Same-side interior angles sum to $180^\circ$.
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In a triangle, angles are $50^\circ$ and $65^\circ$; what is the third angle?
In a triangle, angles are $50^\circ$ and $65^\circ$; what is the third angle?
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$65^\circ$. Triangle angles sum to $180^\circ$.
$65^\circ$. Triangle angles sum to $180^\circ$.
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In a triangle, an exterior angle is $120^\circ$ and one remote interior angle is $50^\circ$; what is the other?
In a triangle, an exterior angle is $120^\circ$ and one remote interior angle is $50^\circ$; what is the other?
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$70^\circ$. Exterior angle theorem: $120^\circ = 50^\circ + x$.
$70^\circ$. Exterior angle theorem: $120^\circ = 50^\circ + x$.
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What is the sum of the interior angles of a pentagon ($n=5$)?
What is the sum of the interior angles of a pentagon ($n=5$)?
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$540^\circ$. Using $(n-2) \cdot 180^\circ$ with $n=5$.
$540^\circ$. Using $(n-2) \cdot 180^\circ$ with $n=5$.
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Find the measure of an angle in a regular pentagon.
Find the measure of an angle in a regular pentagon.
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$108^{\text{°}}$. Using formula: $\frac{(5-2)\times180°}{5} = 108°$.
$108^{\text{°}}$. Using formula: $\frac{(5-2)\times180°}{5} = 108°$.
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What is the property of angles on a straight line?
What is the property of angles on a straight line?
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They sum to $180^{\text{°}}$. Linear pair angles are supplementary.
They sum to $180^{\text{°}}$. Linear pair angles are supplementary.
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What is the measure of an angle that is supplementary to $45^{\text{°}}$?
What is the measure of an angle that is supplementary to $45^{\text{°}}$?
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$135^{\text{°}}$. Supplementary angles sum to $180°$, so $180° - 45° = 135°$.
$135^{\text{°}}$. Supplementary angles sum to $180°$, so $180° - 45° = 135°$.
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Identify the angle type if two angles measure $45^{\text{°}}$ and $45^{\text{°}}$.
Identify the angle type if two angles measure $45^{\text{°}}$ and $45^{\text{°}}$.
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Complementary angles. Since $45° + 45° = 90°$.
Complementary angles. Since $45° + 45° = 90°$.
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What is the property of angles around a point?
What is the property of angles around a point?
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They sum to $360^{\text{°}}$. Full rotation around any point equals $360°$.
They sum to $360^{\text{°}}$. Full rotation around any point equals $360°$.
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What is the measure of an angle in a regular dodecagon?
What is the measure of an angle in a regular dodecagon?
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$150^{\text{°}}$. Using formula: $\frac{(12-2)\times180°}{12} = 150°$.
$150^{\text{°}}$. Using formula: $\frac{(12-2)\times180°}{12} = 150°$.
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Find the measure of each angle in a regular triangle.
Find the measure of each angle in a regular triangle.
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$60^{\text{°}}$. Regular triangle means equilateral triangle.
$60^{\text{°}}$. Regular triangle means equilateral triangle.
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What is the measure of a straight angle?
What is the measure of a straight angle?
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$180^\circ$. Half a complete rotation.
$180^\circ$. Half a complete rotation.
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What is the measure of a right angle?
What is the measure of a right angle?
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$90^\circ$. Quarter of a complete rotation.
$90^\circ$. Quarter of a complete rotation.
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