Question

Match the following columns:

Column I	Column II
(a) If x° and y° be the measures of two complementary angles, such that 2x = 3y, then x = .......	(p) 45°
(b) If an angle is the supplement of itself, then the measure of the angle is .......	(q) 60°
(c) If an angle is the complement of itself, then the measure of the angle is .......	(r) 54°
(d) If x° and y° be the angles forming a linear pair, such that x − y = 60°, then = ........	(s) 90°

(a) ......,
(b) ......,
(c) ......,
(d) ......,

Answer 1

(a)
We have :
$$\begin{gathered} x+y=90° \\ \Rightarrow x+\frac{2}{3}x=90°\left[\because 2x=3y\right] \\ \Rightarrow 3x+2x=270° \\ \Rightarrow 5x=270° \\ \Rightarrow x=54° \end{gathered}$$
Hence, (a)$\mathbf{\Rightarrow }$(r).

(b)
We have :
$$\begin{gathered} x+x=180° \\ \Rightarrow 2x=180° \\ \Rightarrow x=90° \end{gathered}$$
Hence, (b)$\mathbf{\Rightarrow }$(s).

(c)
We have :
$$\begin{gathered} x+x=90° \\ \Rightarrow 2x=90° \\ \Rightarrow x=45° \end{gathered}$$
Hence, (c)$\mathbf{\Rightarrow }$(p).

(d)
We have:
$$\begin{gathered} x+y=180°...\left(i\right)\left[\text{Linear pair}\right] \\ x-y=60°...\left(ii\right)\left[\text{Given}\right] \\ \mathrm{Adding}\left(i\right)\mathrm{and}\left(ii\right),\text{we get:} \\ 2y=120° \\ \Rightarrow y=60° \end{gathered}$$
Hence, (d)$\mathbf{\Rightarrow }$(q).