Section 3.2 & 3.3

Section 3.2 & 3.3 Section 3.2 Answer: m ∠ 1 = ∠ 150 º ( Vertically Opposite AnglesTheorem ) m ∠ 1 = m ∠ 2 ( Corresponding Angles Theorem ) . ∴ m ∠ 1 = m ∠ 2 = 150 º Answer: Since, ∠ (7 x +24) º and ∠ 72 ∘ are Consecutive Interior Angles . Therefore, ∠ (7 x +24) ∘ + ∠ 72 ∘ =180 ∘ ⟹ 7 x +24+72=180 ∘ ⟹ 7 x = (180−96) ∘ ⟹ 7 x =84 ∘ ⟹ x =12

Answer: Since, m ∠ 4 and ∠ 118 ∘ are Linear Pair. Therefore, m ∠ 4+118 ∘ =180 ∘ ⟹ m ∠ 4=62 ∘ Also, m ∠ 4 and ∠ (8 x +6) ∘ are Alternate Interior Angles. Therefore, m ∠ 4= ∠ (8 x +6) ⟹ 8 x +6=62 ∘ ⟹ 8 x =56 ∘ ⟹ x =7 Answer: Since, m ∠ 2 and ∠ 133 ∘ are Alternate Interior Angles. Therefore, m ∠ 2=133 ∘ Also, m ∠ 3 and ∠ 133 ∘ are Consecutive Interior Angles. Therefore, m ∠ 3+133 ∘ =180 ∘ ⟹ m ∠ 3=47 ∘ Also, m ∠ 1 and m ∠ 3 are Alternate Interior Angles.

Therefore, m ∠ 1=m ∠ 3=47 ∘ m ∠1 = m∠3 = 47º and m ∠ 2=133 ∘ Answer: By using Alternate interior angles theorem and Consecutive Interior Angles Theorem, we get: m ∠ 2=70 ∘ and m ∠ 3=110 ∘.