Question

Consider the figure below where CS is parallel BM

Answer 1

Part A: 146°

Part B: 70°

Part C: 104°

Explanation:

Part A:

m<SHI = 34° (given)

m<SHI + m<MIH = 180° (same side interior angles of a transversal are supplementary)

34° + m<MIH = 180° (Substitution)

Subtract 34° from each side

m<MIH = 180° - 34°

m<MIH = 146°

Part B:

m<HAL = 110° (given)

m<HAV + m<HAL = 180° (linear pair)

m<HAV + 110° = 180° (substitution)

Subtract 110° from each side

m<HAV = 180° - 110°

m<HAV = 70°

m<AVM = m<HAV (alternate interior angles are congruent)

m<AVM = 70°

Part C:

The obtuse angle formed = m<HAV + SHI (exterior angle of a triangle = the sum of two opposite interior angles of a ∆)

The obtuse angle formed = 70° + 34° = 104°