Home › Certifications › 7th Math: Geometry › Angle Relationships (Supplementary, Complementary, Vertical, Adjacent)
22 multiple-choice questions and 7 flashcards on Angle Relationships (Supplementary, Complementary, Vertical, Adjacent), about 15% of the 7th Math: Geometry bank. Every one carries a written rationale.
Angle Relationships (Supplementary, Complementary, Vertical, Adjacent) is one of 6 chapters in CoStudy's 7th Math: Geometry bank, and it holds 22 of the bank's 150 multiple-choice questions — roughly 15% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
9 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
Two supplementary angles are in ratio 2:7. The smaller angle measures:
Answer: D — 40°
2x + 7x = 180 → 9x = 180 → x = 20; smaller = 2 × 20 = 40°. (A) found x not 2x; (C) is the larger angle; (B) divided 180 by 9 × 0.5.
A blueprint scale is 1:50. On the drawing, a hallway is 6 cm wide. Actual width?
Answer: D — 300 cm (3 m)
6 × 50 = 300 cm = 3 m. (A) added 50; (C) forgot to multiply the 6; (B) treated 1:50 as 1 cm = 1 m.
Two supplementary angles are in ratio 3:7. The larger is:
Answer: B — 126°
B) 3x + 7x = 180 → x = 18 → 7·18 = 126°. A) Computed 3x. C) Halved 180. D) Used 6x.
Two lines intersect; one angle is 130°. The vertical angle is:
Answer: C — 130°
C) Vertical angles are equal → 130°. A) That's the linear-pair supplement. B) > 180° impossible. D) Halved.
A triangle has exterior angle 120°. The two non-adjacent interior angles are equal. Each measures:
Answer: A — 60°
Exterior angle = sum of two remote interiors → 2x = 120 → x = 60°. (B) halved 60; (C/D) arithmetic errors.
Two angles whose measures sum to 90° are:
Answer: C — Complementary
C) Sum to 90° = complementary. A) Sum to 180°. B) Equal angles from intersecting lines. D) Share a side and vertex but no sum implied.
A square has a perimeter of 36 cm. Its area is:
Answer: B — 81 cm²
Side = 36 ÷ 4 = 9 cm; area = 9² = 81 cm². (A) used P/2; (C) used (P/3)²; (D) confused perimeter with area.
Vertical angles are NEVER:
Answer: C — Different in measure
C) Vertical angles are always congruent. A) They are always equal. B/D) They can be acute or obtuse.
Two angles are supplementary. One is 47°. The other is:
Answer: B — 133°
B) 180 − 47 = 133°. A) Computed complement (90 − 47). C) Arithmetic slip. D) Subtracted from 360°.
4 cards from the 7 in this chapter.
Surface area of a sphere?
SA = 4πr².
WORKED EXAMPLE — Two angles are complementary and form a right angle. One is 38°. Find the other.
STEP 1 — Complementary angles sum to 90°. STEP 2 — Write: 38 + x = 90. STEP 3 — Subtract: x = 90 − 38. STEP 4 — Compute: x = 52°. STEP 5 — Check: 38 + 52 = 90 ✓. ANSWER: 52°.
Surface area of prism?
Sum of all face areas.
WORKED EXAMPLE — Two angles are supplementary. One measures 73°. Find the other.
STEP 1 — Supplementary angles sum to 180°. STEP 2 — Write the equation: 73 + x = 180. STEP 3 — Subtract 73 from both sides: x = 180 − 73. STEP 4 — Compute: x = 107°. STEP 5 — Check: 73 + 107 = 180 ✓. ANSWER: 107°.
These are a sample. The full Angle Relationships (Supplementary, Complementary, Vertical, Adjacent) chapter runs 29 items with per-chapter progress tracking, on the web and in the iOS app.
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