ACT Math Flashcards: Lines And Angles

What this deck covers

This deck focuses on Lines And Angles, giving you a quick way to review the definitions, rules, and examples that matter most for ACT Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the definition of complementary angles?

Answer: Two angles summing to $90^{\text{°}}$. Together they form a right angle.

Flashcard 2: What is the definition of adjacent angles?

Answer: Two angles sharing a vertex and a side with nonoverlapping interiors. Next to each other but don't overlap inside.

Flashcard 3: In a triangle, angles are $50^\circ$ and $65^\circ$; what is the third angle?

Answer: $65^\circ$. Triangle angles sum to $180^\circ$.

Flashcard 4: What is the measure of an angle that is supplementary to $45^{\text{°}}$?

Answer: $135^{\text{°}}$. Supplementary angles sum to $180°$, so $180° - 45° = 135°$.

Flashcard 5: When a transversal cuts parallel lines, what is true about alternate interior angles?

Answer: Alternate interior angles are congruent. Interior angles on opposite sides are equal.

Flashcard 6: When a transversal cuts parallel lines, what is true about corresponding angles?

Answer: Corresponding angles are congruent. Same position angles are equal.

Flashcard 7: What is the relationship between vertical angles formed by two intersecting lines?

Answer: Vertical angles are congruent (equal in measure). Fundamental property of intersecting lines.

Flashcard 8: What is the property of angles on a straight line?

Answer: They sum to $180^{\text{°}}$. Linear pair angles are supplementary.

Flashcard 9: Identify the angle that forms a linear pair with $130^{\text{°}}$.

Answer: $50^{\text{°}}$. Linear pair angles are supplementary, so $180° - 130° = 50°$.

Flashcard 10: How many degrees are in each angle of an equilateral triangle?

Answer: $60^{\text{°}}$. All angles in an equilateral triangle are equal.

Flashcard 11: Find the measure of an angle in a regular pentagon.

Answer: $108^{\text{°}}$. Using formula: $\frac{(5-2)\times180°}{5} = 108°$.

Flashcard 12: Which condition proves two lines are parallel using alternate interior angles?

Answer: If alternate interior angles are congruent, the lines are parallel. Converse of alternate interior angles theorem.

Flashcard 13: What is the measure of each interior angle in a regular heptagon?

Answer: $128.57^\circ$. Using formula: $\frac{(7-2)\times180^\circ}{7} ≈ 128.57^\circ$.

Flashcard 14: What is each interior angle of a regular $n$-gon?

Answer: $\frac{(n-2)\cdot 180^\circ}{n}$. Total interior sum divided by number of sides.

Flashcard 15: What is the sum of the interior angles of a pentagon ($n=5$)?

Answer: $540^\circ$. Using $(n-2) \cdot 180^\circ$ with $n=5$.

Flashcard 16: What is the definition of supplementary angles?

Answer: Two angles summing to $180^{\text{°}}$. Together they form a straight line.

Flashcard 17: What is a transversal?

Answer: A line that intersects two or more other lines. Cuts across multiple lines.

Flashcard 18: What is the formula for the sum of interior angles in an $n$-sided polygon?

Answer: $(n-2) \times 180^{\text{°}}$. Derived from dividing a polygon into triangles.

Flashcard 19: When a transversal cuts parallel lines, what is true about same-side interior angles?

Answer: Same-side interior angles are supplementary. Interior angles on same side add to $180^\circ$.

Flashcard 20: Define corresponding angles in parallel lines.

Answer: Angles in matching corners equal to each other. They're in the same relative position at each intersection.

Flashcard 21: What is the definition of supplementary angles in degrees?

Answer: Two angles whose measures sum to $180^\circ$. Together they form a straight angle.

Flashcard 22: Find the measure of an angle in a regular pentagon.

Answer: $108^{\text{°}}$. Using formula: $\frac{(5-2)\times180°}{5} = 108°$.

Flashcard 23: If corresponding angles measure $(3x+10)^\circ$ and $(5x-30)^\circ$, what is $x$?

Answer: $20$. Set corresponding angles equal and solve.

Flashcard 24: If two angles form a linear pair, what equation relates their measures?

Answer: $m\angle 1 + m\angle 2 = 180^\circ$. Linear pairs always sum to a straight angle.

Flashcard 25: Define alternate exterior angles in parallel lines.

Answer: Non-adjacent and equal angles outside parallel lines. They're on opposite sides of the transversal.

Flashcard 26: Find the measure of each angle in a regular triangle.

Answer: $60^{\text{°}}$. Regular triangle means equilateral triangle.

Flashcard 27: Find the measure of the missing angle if two angles are $90^{\text{°}}$ and $30^{\text{°}}$ in a triangle.

Answer: $60^{\text{°}}$. Triangle angles sum to $180°$, so $180° - 90° - 30° = 60°$.

Flashcard 28: Identify the vertical angle to $60^{\text{°}}$ in an intersecting lines scenario.

Answer: $60^{\text{°}}$. Vertical angles are always equal.

Flashcard 29: What is the measure of each exterior angle of a regular decagon?

Answer: $36^{\text{°}}$. Exterior angle = $\frac{360°}{10} = 36°$ for a decagon.

Flashcard 30: Identify the type of angles if one is $110^{\text{°}}$ and another is $70^{\text{°}}$.

Answer: Supplementary angles. Since $110° + 70° = 180°$.

Flashcard 31: What is the definition of complementary angles in degrees?

Answer: Two angles whose measures sum to $90^\circ$. Together they form a right angle.

Flashcard 32: What is the measure of a straight angle?

Answer: $180^\circ$. Half a complete rotation.

Flashcard 33: Identify the type of angles if one is $110^{\text{°}}$ and another is $70^{\text{°}}$.

Answer: Supplementary angles. Since $110° + 70° = 180°$.

Flashcard 34: What is the measure of a full rotation (one complete turn)?

Answer: $360^\circ$. Complete circle rotation.

Flashcard 35: If two angles are supplementary, what equation relates their measures?

Answer: $m\angle 1 + m\angle 2 = 180^\circ$. Definition of supplementary angles.

Flashcard 36: What is the measure of a full rotation (one complete turn)?

Answer: $360^\circ$. Complete circle rotation.

Flashcard 37: If two lines are perpendicular, what is the measure of the angles formed?

Answer: All four angles measure $90^\circ$. Perpendicular lines form right angles.

Flashcard 38: If two angles form a linear pair and one measures $112^\circ$, what is the other?

Answer: $68^\circ$. Linear pairs sum to $180^\circ$.

Flashcard 39: Identify the angle that forms a linear pair with $130^{\text{°}}$.

Answer: $50^{\text{°}}$. Linear pair angles are supplementary, so $180° - 130° = 50°$.

Flashcard 40: What is the sum of the interior angles of an $n$-gon?

Answer: $(n-2)\cdot 180^\circ$. General polygon angle sum formula.

Flashcard 41: What is the definition of adjacent angles?

Answer: Two angles with a common side and vertex. They share a vertex and one side between them.

Flashcard 42: What is the measure of an angle that is complementary to $30^{\text{°}}$?

Answer: $60^{\text{°}}$. Complementary angles sum to $90°$, so $90° - 30° = 60°$.

Flashcard 43: What is the property of angles on a straight line?

Answer: They sum to $180^{\text{°}}$. Linear pair angles are supplementary.

Flashcard 44: What is the definition of adjacent angles?

Answer: Two angles with a common side and vertex. They share a vertex and one side between them.

Flashcard 45: Which condition proves two lines are parallel using corresponding angles?

Answer: If corresponding angles are congruent, the lines are parallel. Converse of corresponding angles theorem.

Flashcard 46: What is the measure of an angle in a regular dodecagon?

Answer: $150^{\text{°}}$. Using formula: $\frac{(12-2)\times180°}{12} = 150°$.

Flashcard 47: In a triangle, an exterior angle is $120^\circ$ and one remote interior angle is $50^\circ$; what is the other?

Answer: $70^\circ$. Exterior angle theorem: $120^\circ = 50^\circ + x$.

Flashcard 48: If a regular polygon has each exterior angle $24^\circ$, how many sides does it have?

Answer: $15$. Using $n = \frac{360^\circ}{24^\circ}$.

Flashcard 49: What is the definition of complementary angles?

Answer: Two angles summing to $90^{\text{°}}$. Together they form a right angle.

Flashcard 50: What is the measure of an angle that is supplementary to $125^{\text{°}}$?

Answer: $55^{\text{°}}$. Supplementary angles sum to $180°$, so $180° - 125° = 55°$.

Flashcard 51: What is each interior angle of a regular $n$-gon?

Answer: $\frac{(n-2)\cdot 180^\circ}{n}$. Total interior sum divided by number of sides.

Flashcard 52: What is the definition of supplementary angles in degrees?

Answer: Two angles whose measures sum to $180^\circ$. Together they form a straight angle.

Flashcard 53: What is the sum of the interior angles of a quadrilateral?

Answer: $360^{\text{°}}$. Sum of interior angles increases by $180°$ for each additional side.

Flashcard 54: Find the measure of an angle in an equilateral triangle.

Answer: $60^{\text{°}}$. All angles are equal in an equilateral triangle.

Flashcard 55: What is the formula for the sum of interior angles in an $n$-sided polygon?

Answer: $(n-2) \times 180^{\text{°}}$. Derived from dividing a polygon into triangles.

Flashcard 56: What is the sum of the interior angles of a triangle?

Answer: $180^{\text{°}}$. This is a fundamental property of all triangles.

Flashcard 57: When a transversal cuts parallel lines, what is true about alternate exterior angles?

Answer: Alternate exterior angles are congruent. Exterior angles on opposite sides are equal.

Flashcard 58: When a transversal cuts parallel lines, what is true about same-side interior angles?

Answer: Same-side interior angles are supplementary. Interior angles on same side add to $180^\circ$.

Flashcard 59: What is the angle sum of a triangle in degrees?

Answer: $180^\circ$. Fundamental triangle angle property.

Flashcard 60: What is the measure of the exterior angle of a regular nonagon?

Answer: $40^{\text{°}}$. Exterior angle = $\frac{360°}{9} = 40°$ for a nonagon.

Flashcard 61: Which condition proves two lines are parallel using same-side interior angles?

Answer: If same-side interior angles are supplementary, the lines are parallel. Converse of same-side interior theorem.

Flashcard 62: What is each interior angle of a regular hexagon $(n=6)$?

Answer: $120^\circ$. Using $\frac{(n-2) \cdot 180^\circ}{n}$ with $n=6$.

Flashcard 63: Find the measure of the missing angle if two angles are $90^{\text{°}}$ and $30^{\text{°}}$ in a triangle.

Answer: $60^{\text{°}}$. Triangle angles sum to $180°$, so $180° - 90° - 30° = 60°$.

Flashcard 64: What is the property of vertically opposite angles?

Answer: They are equal. Formed by intersecting lines, they're always equal.

Flashcard 65: State the formula to calculate the measure of each interior angle of a regular polygon.

Answer: $\frac{(n-2)\times180}{n}$. Uses the sum of interior angles divided by number of sides.

Flashcard 66: If two angles form a linear pair, what equation relates their measures?

Answer: $m\angle 1 + m\angle 2 = 180^\circ$. Linear pairs always sum to a straight angle.

Flashcard 67: How many degrees are in each angle of an equilateral triangle?

Answer: $60^{\text{°}}$. All angles in an equilateral triangle are equal.

Flashcard 68: If two angles are supplementary and one measures $145^\circ$, what is the other?

Answer: $35^\circ$. Supplementary angles sum to $180^\circ$.

Flashcard 69: Find the missing angle if two angles are $70^{\text{°}}$ and $20^{\text{°}}$ in a triangle.

Answer: $90^{\text{°}}$. Triangle angles sum to $180°$, so $180° - 70° - 20° = 90°$.

Flashcard 70: What is the relationship between alternate interior angles?

Answer: They are equal. When parallel lines are cut by a transversal.

Flashcard 71: Which condition proves two lines are parallel using alternate interior angles?

Answer: If alternate interior angles are congruent, the lines are parallel. Converse of alternate interior angles theorem.

Flashcard 72: What is the measure of each interior angle in a regular heptagon?

Answer: $128.57^{\text{°}}$. Using formula: $\frac{(7-2)\times180°}{7} ≈ 128.57°$.

Flashcard 73: Which condition proves two lines are parallel using corresponding angles?

Answer: If corresponding angles are congruent, the lines are parallel. Converse of corresponding angles theorem.

Flashcard 74: What is the definition of parallel lines in a plane?

Answer: Coplanar lines that never intersect. Same plane, same direction, never meet.

Flashcard 75: Define a linear pair of angles.

Answer: Adjacent angles that form a straight line. They share a side and their sum is $180°$.

Flashcard 76: If two angles form a linear pair and one measures $112^\circ$, what is the other?

Answer: $68^\circ$. Linear pairs sum to $180^\circ$.

Flashcard 77: What is the sum of the exterior angles of any polygon?

Answer: $360^{\text{°}}$. This holds for any polygon regardless of number of sides.

Flashcard 78: What is the property of angles around a point?

Answer: They sum to $360^{\text{°}}$. Full rotation around any point equals $360°$.

Flashcard 79: What is the measure of each angle in a regular decagon?

Answer: $144^{\text{°}}$. Using formula: $\frac{(10-2)\times180°}{10} = 144°$.

Flashcard 80: If two angles are vertical and one measures $37^\circ$, what is the other?

Answer: $37^\circ$. Vertical angles are always congruent.

Flashcard 81: What is the definition of vertical angles?

Answer: Opposite angles formed by intersecting lines; they are congruent. They have equal measures when lines cross.

Flashcard 82: If a regular polygon has each exterior angle $24^\circ$, how many sides does it have?

Answer: $15$. Using $n = \frac{360^\circ}{24^\circ}$.

Flashcard 83: Find the measure of each angle in a regular triangle.

Answer: $60^{\text{°}}$. Regular triangle means equilateral triangle.

Flashcard 84: State the formula to calculate the measure of each interior angle of a regular polygon.

Answer: $\frac{(n-2)\times180}{n}$. Uses the sum of interior angles divided by number of sides.

Flashcard 85: Find the measure of an angle in an equilateral triangle.

Answer: $60^{\text{°}}$. All angles are equal in an equilateral triangle.

Flashcard 86: What is the measure of a straight angle?

Answer: $180^\circ$. Half a complete rotation.

Flashcard 87: What is the definition of complementary angles in degrees?

Answer: Two angles whose measures sum to $90^\circ$. Together they form a right angle.

Flashcard 88: If corresponding angles measure $(3x+10)^\circ$ and $(5x-30)^\circ$, what is $x$?

Answer: $20$. Set corresponding angles equal and solve.

Flashcard 89: What is the sum of the exterior angles of any polygon?

Answer: $360^{\text{°}}$. This holds for any polygon regardless of number of sides.

Flashcard 90: What is the measure of an angle that is complementary to $65^{\text{°}}$?

Answer: $25^{\text{°}}$. Complementary angles sum to $90°$, so $90° - 65° = 25°$.

Flashcard 91: If two angles are supplementary, what equation relates their measures?

Answer: $m\angle 1 + m\angle 2 = 180^\circ$. Definition of supplementary angles.

Flashcard 92: Define an angle bisector.

Answer: A ray dividing an angle into two equal parts. It creates two congruent angles.

Flashcard 93: What is the exterior angle theorem for a triangle?

Answer: An exterior angle equals the sum of the two remote interior angles. Exterior equals sum of non-adjacent interior angles.

Flashcard 94: Find the measure of an angle in a regular nonagon.

Answer: $140^{\text{°}}$. Using formula: $\frac{(9-2)\times180°}{9} = 140°$.

Flashcard 95: What is the sum of the interior angles of a pentagon ($n=5$)?

Answer: $540^\circ$. Using $(n-2) \cdot 180^\circ$ with $n=5$.

Flashcard 96: What is the definition of supplementary angles?

Answer: Two angles summing to $180^{\text{°}}$. Together they form a straight line.

Flashcard 97: What is the exterior angle theorem for a triangle?

Answer: An exterior angle equals the sum of the two remote interior angles. Exterior equals sum of non-adjacent interior angles.

Flashcard 98: What is the definition of vertical angles?

Answer: Opposite angles formed by intersecting lines; they are congruent. They have equal measures when lines cross.

Flashcard 99: Define corresponding angles in parallel lines.

Answer: Angles in matching corners equal to each other. They're in the same relative position at each intersection.

Flashcard 100: What is a transversal?

Answer: A line that intersects two or more other lines. Cuts across multiple lines.