Question

The angles of a quadrilateral are 3x°, (x + 30)°, (x - 30)° and (2x + 10)°. The value of the smallest angle is .

• A. 80°
• B. 150°
• C. 110°
• D. 20°

Answer 1

The correct option is D 20°

By angle sum property, the sum of interior angles of a quadrilateral is 360°.

If ABCD is a quadrilateral, then
$\Rightarrow \angle A+\angle B+\angle C+\angle D=360°\Rightarrow 3x°+(x+30)°+(x-30)°+(2x+10)°=360°\Rightarrow 3x°+x°+x°+2x°+(30-30+10)°=360°\Rightarrow 7x°=360°-10°=350°\Rightarrow x°=50°$

So, the angles of the quadrilateral are,
$3x°=3\left(50°\right)=150°,(x+30)°=(50°+30°)=80°,(x-30)°=(50-30)°=20°,(2x+10)°=(2\times 50+10)°=(100+10)°=110°.$

Hence, the smallest angle of the quadrilateral is 20°.