Angles & Lines
What kind of angle is 90°?
Right angle
Find the perimeter of a rectangle with length 8 and width 3.
P = 2(8 + 3) = 22
Name the point at (0, 0).
Origin
Evaluate: 4 + 3 × 2
10
Solve: x + 6 = 14
x = 8
Two angles form a straight line. One is 55°. What is the other?
125°
Find the area of a rectangle with length 9 and width 4.
A = 9×4 = 36
What quadrant is (−3, 5) in?
Quadrant II
Simplify: 6a + 2a
8a
3x = 27
x = 9
A triangle has angles 35° and 65°. What is the third angle?
80° (since 180 − 35 − 65)
A square has perimeter 36. What is its area?
Perimeter 36 → side 9 → area 81
Start at (2, −1). Move left 5 and up 3. Where do you land?
The rule is “multiply by 3, then subtract 2.” What’s the output when the input is 6?
16
Solve: 2x + 5 = 21
2x = 16 → x = 8
Angle A is 3 times Angle B. Together they make 180°. Find Angle A and Angle B.
B = 45°, A = 135° (since A = 3B and A + B = 180 → 4B = 180)
A rectangle has area 48 and width 6. What is its perimeter?
Area 48, width 6 → length 8 → perimeter 2(8 + 6)=28
What is the distance (in unit steps) between (−2, 4) and (3, 4)?
5 units (same y-value, horizontal distance)
Simplify: 3(x + 4) + 2x
3x + 12 + 2x = 5x + 12
A number n is multiplied by 4 then increased by 9 to get 37. Write and solve an equation.
4n + 9 = 37 → 4n = 28 → n = 7
Two complementary angles differ by 26°. Find both angles.
Let angles be x and x + 26, x + (x + 26) = 90 → 2x = 64 → x = 32°, other 58°
A rectangle’s length is (w + 5). Its width is w. If the perimeter is 34, find w, then the area.
Perimeter 34 → 2((w + 5) + w) = 34 → 2(2w + 5) = 34 → 4w + 10 = 34 → w = 6 → length 11 → area 66
A point is equally far from (1, 2) and (5, 2) on the same horizontal line. What are the possible points (give at least 2)?
Midpoint on that horizontal line is x = 3, y = 2 → (3,2) is one; “equally far” on same horizontal line generally means any point on the vertical line x = 3 (e.g., (3,2), (3,0), (3,5), etc.). If you want to restrict to the segment between them, then (3,2) only.
The expression 2x + 10 is equal to 4(x − 1). Solve for x.
2x + 10 = 4x − 4 → 14 = 2x → x=7
Maya buys 3 notebooks and a pen for $17. The pen costs $2. Each notebook costs the same. Write and solve an equation. Then explain what the solution means.
3n + 2 = 17 → 3n = 15 → n = 5; each notebook costs $5