- A70°
- B35°
- C65°
- D45°
Step-by-Step Solution
An exterior angle equals the sum of the two interior opposite angles: . So .
Answer: A) 70°
In triangle ABC, side BC is produced to D. The exterior angle ∠ACD = 115°, ∠ABC = ° and ∠BAC = . Find ∠BAC.
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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