Question

In the figure given alongside, x : y = 2 : 3 and ∠ACD = 130°.
Find the values of x, y and z.

Answer 1

$$\begin{gathered} \frac{x}{y}=\frac{2}{3} \\ \Rightarrow 3x=2y \\ \Rightarrow x=\frac{2}{3}y \end{gathered}$$

We know that the exterior angle of a triangle is equal to the sum of the interior opposite angles.


∴ $\angle A+\angle B=\angle ACD$

x$°$+ y$°$ = 130$°$

$$\begin{gathered} \Rightarrow \frac{2y}{3}+y=130 \\ \Rightarrow 5y=130\times 3 \\ \Rightarrow 5y=390 \\ \Rightarrow y=78 \\ \Rightarrow x=\frac{2}{3}\times 78 \\ \Rightarrow x=52 \end{gathered}$$

Also, sum of the angles in any triangle is 180$°$
∴ x+ y + z = 180
z= 180- 78 - 52
z= 50