  Question

Which of the following statements are true (T)  and which are false (F)? (i) Angles forming a linear pair are supplementary. (ii) If two adjacent angles are equal, then each angle measures 90°. (iii) Angles forming a linear pair can both be acute angles. (iv) If angles forming a linear pair are equal, then each of these angles is of measure 90°.

Solution

(i) True As the sum of the angles forming a linear pair is . (ii) False As the statement is incomplete in itself. (iii) False Let us assume one of the angle in a linear pair be ; such that ,that is, an acute angle. Therefore, the other angle in the linear pair becomes , which clearly cannot be acute. (iv) True Let one of the angle in the linear pair be . Then, other angle also becomes equal to . Therefore, by the definition of linear pair, we get: . Hence, if angles forming a linear pair are equal, then each of these angles is of measure . MathematicsRD Sharma (2017)Standard IX

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