Question

in triangle ABC, angle A + angle B = 122 degrees and angle B + angle C = 111 degrees. find the measure of angle B and angle C

Answer 1

$$\begin{gathered} \angle \mathrm{A}+\angle \mathrm{B}=122°...\left(1\right) \\ \angle \mathrm{B}+\angle \mathrm{C}=111°...\left(2\right) \\ \angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180°...\left(3\right)\left(\mathrm{Angle}\mathrm{Sum}\mathrm{Property}\right) \\ \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}\left(\angle \mathrm{A}+\angle \mathrm{B}\right)\mathrm{from}\left(1\right)\mathrm{in}\left(3\right) \\ 122°+\angle \mathrm{C}=180° \\ \angle \mathrm{C}=180°-122° \\ \angle \mathrm{C}=58° \\ \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}\angle \mathrm{C}\mathrm{in}\left(2\right) \\ \angle \mathrm{B}+58°=111° \\ \angle \mathrm{B}=111°-58° \\ \angle \mathrm{B}=53° \\ \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}\angle \mathrm{B}\mathrm{in}\left(1\right) \\ \angle \mathrm{A}+53°=122° \\ \angle \mathrm{A}=122°-53° \\ \angle \mathrm{A}=69° \\ \mathrm{Measure}\mathrm{of}\angle \mathrm{B}\mathrm{is}53°\mathrm{and}\mathrm{of}\angle \mathrm{C}\mathrm{is}58°. \end{gathered}$$