question_answer 1)

Identify which of the following pairs of angles are complementary and which are supplementary. (i) \[\text{6}{{\text{5}}^{o}},\text{11}{{\text{5}}^{o}}\]                                 (ii) \[\text{6}{{\text{3}}^{o}},\text{ 2}{{\text{7}}^{o}}\]                         (iii) \[{{112}^{o}},{{68}^{o}}\]                      (iv) \[\text{13}{{0}^{o}},\text{5}{{0}^{o}}\]  (v) \[\text{4}{{\text{5}}^{o}}\text{, 4}{{\text{5}}^{o}}\]                                 (vi) \[\text{8}{{0}^{o}},\text{ 1}{{0}^{o}}\].                

Answer:

                (i) \[\mathbf{6}{{\mathbf{5}}^{\mathbf{o}}}\mathbf{, 11}{{\mathbf{5}}^{\mathbf{o}}}\] \[\because \]     \[\text{6}{{\text{5}}^{o}}+\text{11}{{\text{5}}^{o}}=\text{18}{{0}^{o}}\] \[\therefore \]  The given pair of angles are supplementary. (ii) \[\mathbf{6}{{\mathbf{3}}^{\mathbf{o}}}\mathbf{, 2}{{\mathbf{7}}^{\mathbf{o}}}\] \[\because \]     \[\text{6}{{\text{3}}^{o}}+\text{2}{{\text{7}}^{o}}=\text{9}{{0}^{o}}\] \[\therefore \] The given pair of angles are complementary. (iii) \[\mathbf{11}{{\mathbf{2}}^{\mathbf{o}}}\mathbf{, 6}{{\mathbf{8}}^{\mathbf{o}}}\] \[\because \]     \[\text{11}{{\text{2}}^{o}}+\text{6}{{\text{8}}^{o}}=\text{18}{{0}^{o}}\] \[\therefore \]  The given pair of angles are supplementary. (iv) \[\mathbf{13}{{\mathbf{0}}^{\mathbf{o}}}\mathbf{, 5}{{\mathbf{0}}^{\mathbf{o}}}\] \[\because \]     \[\text{13}{{0}^{o}}+\text{5}{{0}^{o}}=\text{18}{{0}^{o}}\] \[\therefore \] The given pair of angles are supplementary. (v) \[\mathbf{4}{{\mathbf{5}}^{\mathbf{o}}}\mathbf{, 4}{{\mathbf{5}}^{\mathbf{o}}}\] \[\because \]     \[{{45}^{o}}+{{45}^{o}}={{90}^{o}}\] \[\therefore \]  The given pair of angles are complementary. (vi) \[\mathbf{8}{{\mathbf{0}}^{\mathbf{o}}}\mathbf{, 1}{{\mathbf{0}}^{\mathbf{o}}}\] \[\because \]     \[\text{8}{{0}^{o}}+\text{1}0=\text{9}{{0}^{o}}\]  \[\therefore \] The given pair of angles are complementary.