Question

In Fig, two of the angles are indicated. What are the measures of ∠ACX and ∠ACB?

Answer 1

$$\begin{gathered} \mathrm{In}∆\mathrm{ABC},\angle \mathrm{A}=50°\mathrm{and}\angle \mathrm{B}=55°. \\ \mathrm{Because}\mathrm{of}\mathrm{the}\mathrm{angle}\mathrm{sum}\mathrm{property}\mathrm{of}\mathrm{the}\mathrm{triangle},\mathrm{we}\mathrm{can}\mathrm{say}\mathrm{that}: \\ \angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180° \\ \Rightarrow 50°+55°+\angle \mathrm{C}=180° \\ \mathrm{Or}, \\ \angle \mathrm{C}=75° \\ \mathrm{i}.\mathrm{e}.\angle \mathrm{ACB}=75° \\ \angle \mathrm{ACX}=180°-\angle \mathrm{ACB}=180°-75°=105°(\mathrm{Linear}\mathrm{pair}) \end{gathered}$$