Question

Find the values of the unknown $$x$$ and $$y$$ in the following diagram.

Answer 1

$$\textbf{Step 1: Find the required angles applying suitable properties.}$$

$$\text{In the diagram angles measuring y and } 120^\circ \text{ are linear pair.}$$

$$\text{We know, linear pair are supplementary.}$$

$$\therefore y+120^\circ=180^\circ$$

$$\Rightarrow y=60^\circ......(1)$$

$$\text{We know, sum of interior angles of a triangles is }180^\circ.$$

$$\text{So, from the given triangle, }$$

$$\therefore x+y+50^\circ=180^\circ$$

$$\Rightarrow x+60^\circ=130^\circ$$ $$[\textbf{From (1)}]$$

$$\Rightarrow x=70^\circ$$

$$\mathbf{\textbf{Hence, the values of x and y are } 70^\circ\ and \ 60^\circ\ respectively.}$$