Directions: Quantitative Comparison - compare Quantity A and Quantity B, using the information below, and select one of the following four answer choices.
α and β are complementary angles; γ and α are supplementary angles; δ and β are also supplementary angles. (R = 90°)
Quantity A: γ + δ
Quantity B: 3R
Correct Answer : C
Question: α and β are complementary angles; γ and α are supplementary angles; δ and β are also supplementary angles. (R = 90°)
Quantity A: γ + δ
Quantity B: 3R
α and β are complementary angles; γ and α are supplementary angles; δ and β are also supplementary angles. (R = 90°)
Quantity A: γ + δ
Quantity B: 3R
Correct Answer : C
Question: α and β are complementary angles; γ and α are supplementary angles; δ and β are also supplementary angles. (R = 90°)
Quantity A: γ + δ
Quantity B: 3R
Explanation: We are given
α + β = 90°
γ + α = 180°
δ + β = 180°
Therefore β = 90° - &alpha
δ = 180° - β = 180° - (90° - α) = 180° - 90° + α
δ = 90° + α; &alpha = δ - 90°
γ + α = 180°
γ + δ - 90° = 180°
γ + δ = 180° + 90°
γ + δ = 270°
3R = 3 x 90° = 270°
α + β = 90°
γ + α = 180°
δ + β = 180°
Therefore β = 90° - &alpha
δ = 180° - β = 180° - (90° - α) = 180° - 90° + α
δ = 90° + α; &alpha = δ - 90°
γ + α = 180°
γ + δ - 90° = 180°
γ + δ = 180° + 90°
γ + δ = 270°
3R = 3 x 90° = 270°
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