8th grade · Math · Unit 8 of 19
Angle Detective
Parallel lines and polygons
What your child practices
Using equal and supplementary angles when a transversal crosses parallel lines, and the angle sums of triangles, quadrilaterals and polygons, including exterior angles.
New York State Learning Standards learning standard: NY-8.G.5 · angle sums of triangles and angles formed by parallel lines
How we explain it
Children can open this short lesson before they practice.
- Angles on a straight line add to 180°.
- The angles in a triangle add to 180°.
- When two lines cross, opposite angles are equal.
Example: Two angles on a straight line: one is 115°. What is the other? Together they make 180°. 180 − 115 = 65. Answer: 65°
Angle Detective in New York
In the New York State Learning Standards, this is unit 8 of 19 in 8th grade Math, after Tessellations & Transformations and before Similarity & Scale.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
A transversal crosses two parallel lines. One angle measures 112°. How many degrees is an alternate interior angle to it?
answer box°
112 °
Hint: These angles are equal when the lines are parallel.
Question 2
What is the sum of the interior angles of a polygon with 12 sides?
answer box°
1800 °
Hint: Split it into triangles: (n − 2) × 180° = 10 × 180°.
Question 3
What is the measure of each interior angle of a regular polygon with 10 sides?
answer box°
144 °
Hint: Find the sum, 1440°, then divide by 10.
Question 4
What is the measure of each exterior angle of a regular polygon with 6 sides?
answer box°
60 °
Hint: The exterior angles of any polygon add to 360°. Divide 360° by 6.
Question 5
Two co-interior angles between parallel lines measure (x + 27)° and (3x + 33)°. What is x?
answer box
30
Hint: Co-interior angles add to 180°. Solve x + 27 + 3x + 33 = 180.
Question 6
In a triangle, two interior angles are 38° and 36°. What is the exterior angle at the third vertex?
answer box°
74 °
Hint: An exterior angle equals the sum of the two opposite interior angles: 38 + 36.