Question

The three angles of a quadrilateral are respectively equal to ${110}^{\circ },{50}^{\circ }$ and ${40}^{\circ }.$ Find its fourth angle.

Answer 1

$\because$ The sum of four angles of a quadrilateral = ${360}^{\circ }$
Three angles are ${110}^{\circ },{50}^{\circ }$ and ${40}^{\circ }$
Let fourth angle =x
Then ${110}^{\circ }+{50}^{\circ }+{40}^{\circ }+x^{\circ }={360}^{\circ }\Rightarrow {200}^{\circ }+x^{\circ }={360}^{\circ }\Rightarrow x^{\circ }={360}^{\circ }-{200}^{\circ }={160}^{\circ }\therefore x={160}^{\circ }$ Ans.