Question

If (3x-15)degree and (x+5)degree are complementary angles then find the angles.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{complementary}\mathrm{angles}\mathrm{add}\mathrm{up}\mathrm{to}90°. \\ \mathrm{Let}\angle \mathrm{A}=\left(3\mathrm{x}-15\right)°\mathrm{and}\angle \mathrm{B}=\left(\mathrm{x}+5\right)° \\ \mathrm{Now},\angle \mathrm{A}\mathrm{and}\angle \mathrm{B}\mathrm{are}\mathrm{complementary}\mathrm{angles},\mathrm{then} \\ \angle \mathrm{A}+\angle \mathrm{B}=90° \\ \Rightarrow \left(3\mathrm{x}-15\right)°+\left(\mathrm{x}+5\right)°=90° \\ \Rightarrow 4\mathrm{x}-10°=90° \\ \Rightarrow 4\mathrm{x}=90°+10° \\ \Rightarrow 4\mathrm{x}=100° \\ \Rightarrow \mathrm{x}=\frac{1}{4}\times 100°=25° \end{gathered}$$