8th Grade Math Flashcards: Establish Angle Facts Using Arguments

What this deck covers

This deck focuses on Establish Angle Facts Using Arguments, giving you a quick way to review the definitions, rules, and examples that matter most for 8th Grade 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: When two parallel lines are cut by a transversal, what is true about same-side (consecutive) interior angles?

Answer: They are supplementary: sum is $180^\circ$. They're on the same side of the transversal between parallels.

Flashcard 2: Find $x$ if alternate interior angles are $5x-15$ and $3x+25$ degrees for parallel lines.

Answer: $x=20$. Alternate interior angles are equal: $5x - 15 = 3x + 25$.

Flashcard 3: Find the third angle of a triangle if two angles are $x^\circ$ and $x^\circ$ and the third is $40^\circ$; find $x$.

Answer: $x=70^\circ$. $x + x + 40 = 180°$, so $2x = 140°$.

Flashcard 4: Identify whether triangles are similar by AA if one has angles $40^\circ$ and $70^\circ$ and the other has $40^\circ$ and $70^\circ$.

Answer: Yes, they are similar by $AA$. Two pairs of equal angles satisfy the AA criterion.

Flashcard 5: Find $x$ if same-side interior angles are $2x+20$ and $3x+10$ degrees for parallel lines.

Answer: $x=30$. Same-side angles sum to $180°$: $(2x + 20) + (3x + 10) = 180°$.

Flashcard 6: Find $x$ if corresponding angles formed by a transversal are labeled $3x+10$ and $7x-30$ degrees.

Answer: $x=10$. Corresponding angles are equal: $3x + 10 = 7x - 30$.

Flashcard 7: Find $x$ if an exterior angle is $140^\circ$ and its adjacent interior angle is $x^\circ$.

Answer: $x=40^\circ$. $140° + x = 180°$ since they're supplementary.

Flashcard 8: Find the exterior angle measure if the two remote interior angles are $35^\circ$ and $75^\circ$.

Answer: $110^\circ$. Exterior angle equals the sum of remote interior angles.

Flashcard 9: Find $x$ if an exterior angle of a triangle is $110^\circ$ and one remote interior angle is $45^\circ$.

Answer: $x=65^\circ$. $110° = 45° + x$, so $x = 110° - 45°$.

Flashcard 10: Find $x$ if the interior angles of a triangle are $50^\circ$, $60^\circ$, and $x^\circ$.

Answer: $x=70^\circ$. $50° + 60° + x = 180°$, so $x = 180° - 110°$.

Flashcard 11: What is always true about a linear pair of angles?

Answer: They are supplementary: sum is $180^\circ$. Adjacent angles that form a straight line.

Flashcard 12: What is always true about vertical angles formed by two intersecting lines?

Answer: Vertical angles are congruent. Opposite angles formed by intersecting lines are always equal.

Flashcard 13: When two parallel lines are cut by a transversal, which angle pair is always congruent: alternate interior angles or same-side interior angles?

Answer: Alternate interior angles are congruent. They form a Z-pattern and are equal when lines are parallel.

Flashcard 14: When two parallel lines are cut by a transversal, which angle pair is always congruent: corresponding angles or adjacent angles?

Answer: Corresponding angles are congruent. They occupy the same position relative to the transversal.

Flashcard 15: What is the angle-angle similarity criterion for triangles?

Answer: If two angles are congruent, the triangles are similar. Two pairs of equal angles guarantee the third pair is also equal.

Flashcard 16: What is the measure of each exterior angle of an equilateral triangle?

Answer: Each exterior angle is $120^\circ$. Each supplements its adjacent $60°$ interior angle.

Flashcard 17: What is the measure of each interior angle in an equilateral triangle?

Answer: Each interior angle is $60^\circ$. All three equal angles must sum to $180°$, so each is $180° ÷ 3$.

Flashcard 18: Identify the relationship between an exterior angle and its adjacent interior angle in a triangle.

Answer: They are supplementary: sum is $180^\circ$. They form a straight angle on the same line.

Flashcard 19: What is the exterior angle of a triangle equal to in terms of the two remote interior angles?

Answer: Exterior angle $=$ sum of the two remote interior angles. Forms a straight line with the adjacent interior angle.

Flashcard 20: What is the sum of the interior angles of any triangle?

Answer: $180^\circ$. The three angles of any triangle always add up to a straight angle.

Flashcard 21: Find the adjacent interior angle if an exterior angle of a triangle is $118^\circ$.

Answer: $62^\circ$. $180^\circ - 118^\circ = 62^\circ$ since they form a linear pair.

Flashcard 22: Find the exterior angle of a triangle if the two remote interior angles are $50^\circ$ and $60^\circ$.

Answer: $110^\circ$. $50^\circ + 60^\circ = 110^\circ$ using the exterior angle theorem.

Flashcard 23: Identify whether triangles are similar by AA: Triangle $1$ has angles $40^\circ,70^\circ$; Triangle $2$ has $40^\circ,70^\circ$.

Answer: Yes, similar by $AA$. Two pairs of congruent angles satisfy the AA criterion.

Flashcard 24: 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 $x$.

Answer: $x=65^\circ$. Similar triangles have all corresponding angles congruent.

Flashcard 25: Two lines are parallel. If a same-side interior angle is $112^\circ$, what is the other same-side interior angle?

Answer: $68^\circ$. $180^\circ - 112^\circ = 68^\circ$ since they're supplementary.

Flashcard 26: Two lines are parallel. If an alternate interior angle is $105^\circ$, what is its alternate interior partner?

Answer: $105^\circ$. Alternate interior angles are congruent when lines are parallel.

Flashcard 27: Two lines are parallel. If a corresponding angle is $72^\circ$, what is the measure of its corresponding partner?

Answer: $72^\circ$. Corresponding angles are congruent when lines are parallel.

Flashcard 28: Find the measure of each angle in an equilateral triangle.

Answer: Each angle is $60^\circ$. $180^\circ \div 3 = 60^\circ$ since all angles are equal.

Flashcard 29: Find the third angle of a triangle if two angles are $65^\circ$ and $45^\circ$.

Answer: $70^\circ$. $180^\circ - 65^\circ - 45^\circ = 70^\circ$ using the triangle angle sum.

Flashcard 30: Find the remote interior angle if an exterior angle is $130^\circ$ and the other remote interior angle is $55^\circ$.

Answer: $75^\circ$. $130^\circ - 55^\circ = 75^\circ$ using the exterior angle theorem.