Question

Reena draws a triangle ABC, obtuse angled at A. What could be the sum of measures of angle B and Angle C? Explain
A. 110
B. 95
C. 90
D. 88

Answer 1

Dear Student,
Here is the solution of your asked query:
$$\begin{gathered} \mathrm{Since},\angle \mathrm{A}\mathrm{is}\mathrm{any}\mathrm{obtuse}\mathrm{angle}\mathrm{so}\angle \mathrm{A}>90° \\ \mathrm{And}\mathrm{we}\mathrm{know}\mathrm{that}\mathrm{sum}\mathrm{of}\mathrm{angles}\mathrm{of}\mathrm{triangle}\mathrm{is}180° \\ \mathrm{So},\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180° \\ \mathrm{Since}\angle \mathrm{A}>90°\mathrm{then}\left(\angle \mathrm{B}+\angle \mathrm{C}\right)<90° \\ \mathrm{Therefore},\mathrm{sum}\mathrm{of}\mathrm{measures}\mathrm{of}\angle \mathrm{B}\mathrm{and}\angle \mathrm{C}\mathrm{could}\mathrm{be}88° \end{gathered}$$
Regards