Question

Find the value of 'a' in each of the following figures.

Answer 1

(i)
$$\begin{gathered} \angle \mathrm{A}+\angle \mathrm{V}+\angle \mathrm{T}=180°(\mathrm{Angle}\mathrm{sum}\mathrm{property}) \\ \Rightarrow a°+a°+40°=180° \\ \Rightarrow 2a°=180°-40° \\ \Rightarrow 2a°=140° \\ \Rightarrow a°=70° \\ \Rightarrow a=70 \end{gathered}$$

(ii)
$$\begin{gathered} \angle \mathrm{U}+\angle \mathrm{P}+\angle \mathrm{X}=180°(\mathrm{Angle}\mathrm{sum}\mathrm{property}) \\ \Rightarrow 50°+90°+a°=180° \\ \Rightarrow a°=180°-140° \\ \Rightarrow a°=40° \\ \Rightarrow a=40 \end{gathered}$$

(iii)
$$\begin{gathered} \angle \mathrm{A}+\angle \mathrm{P}+\angle \mathrm{T}=180°(\mathrm{Angle}\mathrm{sum}\mathrm{property}) \\ \Rightarrow 110°+25°+a°=180° \\ \Rightarrow a°=180°-135° \\ \Rightarrow a°=45° \\ \Rightarrow a=45 \end{gathered}$$