Question

If the angles of a quadrilateral are ${80}^{\circ }$,${110}^{\circ }$,${70}^{\circ }$, then the fourth angle will be ______.

• A. ∠A = 80°, ∠B = 120°, ∠C = 60°, ∠D = 100°
• B. ∠A = 70°, ∠B = 130°, ∠C = 60°, ∠D = 90°
• C. ∠A = 70°, ∠B = 110°, ∠C = 80°, ∠D = 110°
• D. ∠A = 40°, ∠B = 130°, ∠C = 90°, ∠D = 60°

Answer 1

The correct option is A

∠A = 80°, ∠B = 120°, ∠C = 60°, ∠D = 100°

Sum of angles of a quadrilateral is ${360}^{\circ }$.
Let the unknown angle be $x$
$\Rightarrow$ ${80}^{\circ }$+${110}^{\circ }$+${70}^{\circ }$+$x^{\circ }$ = ${360}^{\circ }$
$\Rightarrow$${260}^{\circ }$+$x^{\circ }$ = ${360}^{\circ }$
$\Rightarrow$$x^{\circ }$ = ${360}^{\circ }$-${260}^{\circ }$
$\Rightarrow$$x^{\circ }$ = ${100}^{\circ }$