Two complementary angles differ by 14°. The larger angle is

(a) 50°
(b) 52°
(c) 54°
(d) 56°

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Solution

$(b) 52 ° \begin{array}{l} Let the two complementary angles be x ° and (90 - x) ° . \\ According to the question, we have: \\ x - (90 - x) = 14 \\ ⇒2 x = 104 \\ \Rightarrow x = 52 \\ \Rightarrow (90 - x) ° = 90 ° - 52 ° = 38 ° \\ ∴ The larger angle is 52 ° . \end{array}$

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Two complementary angles differ by 14°. The larger angle is (a) 50° (b) 52° (c) 54° (d) 56°

(b) 52°Let the two complementary angles be x° and (90−x)°.According to the question, we have: x−(90−x)=14⇒2x=104⇒x=52⇒(90−x)°=90°−52°=38°∴The larger angle is 52°.

Two complementary angles differ by 14°. The larger angle is

(a) 50°
(b) 52°
(c) 54°
(d) 56°

$(b) 52 ° \begin{array}{l} Let the two complementary angles be x ° and (90 - x) ° . \\ According to the question, we have: \\ x - (90 - x) = 14 \\ ⇒2 x = 104 \\ \Rightarrow x = 52 \\ \Rightarrow (90 - x) ° = 90 ° - 52 ° = 38 ° \\ ∴ The larger angle is 52 ° . \end{array}$