Question

Match the following figures with their respective values of x.

• A. 85°
• B. 80°
• C. 95°

Answer 1

Case 1:
By linear pair property, $\angle BDC=(180-120)°=60°$
By angle sum property, the sum of interior angles of a quadrilateral is 360°.
$\Rightarrow \angle A+\angle B+\angle C+\angle D=360°$
$x°=360°-(85°+120°+60°)=360°-265°=95°$

Case 2:By angle sum property, the sum of interior angles of a quadrilateral is 360°.
$\Rightarrow \angle A+\angle B+\angle C+\angle D=360°$
$x°=360°-(70°+95°+110°)=360°-275°=85°$

Case 3:By angle sum property, the sum of interior angles of a quadrilateral is 360°.
$\Rightarrow \angle A+\angle B+\angle C+\angle D=360°$
$x°=360°-(95°+93°+92°)=360°-280°=80°$