Question

Question 28
A quadrilateral has three acute angles. If each measures ${80}^{\circ }$, then the measure of the fourth angle is :
a) ${150}^{\circ }$
b) ${120}^{\circ }$
c) ${105}^{\circ }$
d) ${140}^{\circ }$

Answer 1

Let the fourth angle be x, then ${80}^{\circ }+{80}^{\circ }+{80}^{\circ }+x={360}^{\circ }$
[$\because$ sum of all the angles of quadrilaterals is ${360}^{\circ }$]
$\Rightarrow {240}^{\circ }+x={360}^{\circ }\Rightarrow x={360}^{\circ }-{240}^{\circ }\Rightarrow x={120}^{\circ }$