- A38°
- B76°
- C142°
- D104°
Step-by-Step Solution
At B the ray makes with the mirror on both sides, so BC makes with mirror 1. The mirrors are parallel, so BC also makes with mirror 2 (alternate angles), and CD leaves at too. Hence .
Answer: D) 104°
In a science-fair model, Kabir fixes two parallel mirrors facing each other. A light ray AB hits mirror 1 making 38° with it, reflects to C on mirror 2 and leaves along CD. At each mirror the ray makes equal angles before and after reflecting. Find = ∠BCD.
Class 9Lines and AnglesGeometry — Lines and Angles
Key idea: Parallel lines and a transversal — the eight angles
When a transversal cuts two lines, **8 angles** are created (4 at each intersection). They are grouped into four pairs:
**Corresponding angles** — same position relative to each intersection (e.g., upper-left and upper-left).
**Alternate interior angles** — between the two lines, on opposite sides of the transversal.
**Alternate exterior angles** — outside the two lines, on opposite sides of the transversal.
**Co-interior (allied) angles** — between the two lines, on the SAME side of the transversal.
**If the two lines are parallel**:
- Corresponding angles are EQUAL.
- Alternate interior angles are EQUAL.
- Alternate exterior angles are EQUAL.
- Co-interior angles are SUPPLEMENTARY (sum 180°).
**Corresponding angles** — same position relative to each intersection (e.g., upper-left and upper-left).
**Alternate interior angles** — between the two lines, on opposite sides of the transversal.
**Alternate exterior angles** — outside the two lines, on opposite sides of the transversal.
**Co-interior (allied) angles** — between the two lines, on the SAME side of the transversal.
**If the two lines are parallel**:
- Corresponding angles are EQUAL.
- Alternate interior angles are EQUAL.
- Alternate exterior angles are EQUAL.
- Co-interior angles are SUPPLEMENTARY (sum 180°).
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More Class 9 Lines and Angles practice
Three straight streets l, m and n in a Chandigarh sector are parallel (arrow marks) and…Side BC of triangle ABC is produced both ways, to E and to D. The exterior angles are…AB ∥ CD (arrow marks). P is on AB, and Q, R are on CD. ∠APQ = 48° and ∠PRD = 127°. Find…When two parallel lines are cut by a transversal, which pair of angles is SUPPLEMENTARY…An angle whose measure lies strictly between 90° and 180° is classified as which type?