Question

Three angles of a quadrilateral measures: 105${}^{\circ }$, 120${}^{\circ }$ and 75${}^{\circ }$. The measure of the fourth angle is

• A. 60
• B. 65
• C. 55
• D. 70

Answer 1

The correct option is A 60

Sum of all angles of a quadrilateral is ${360}^o$
$\Rightarrow {120}^{\circ }+{105}^{\circ }+{75}^{\circ }+x={360}^{\circ }$
$\Rightarrow {300}^{\circ }+x={360}^{\circ }$
$\Rightarrow x={360}^{\circ }-{300}^{\circ }$
$\Rightarrow x={60}^{\circ }$