Question

Each angle of the given quadrilateral is (x + 5)°.

What type of quadrilateral is ABCD ?

• A. Square
• B. Rectangle
• C. Parallelogram
• D. Rhombus

Answer 1

The correct option is B

Rectangle

$\angle A+\angle B+\angle C+\angle D={360}^{\circ }$

$(x+5{)}^{\circ }+(x+5{)}^{\circ }+(x+5{)}^{\circ }+(x+5{)}^{\circ }={360}^{\circ }$

$4x+{20}^{\circ }={360}^{\circ }$

$4x={360}^{\circ }-{20}^{\circ }={340}^{\circ }$

$x={85}^{\circ }$

$x+5={90}^{\circ }$

$\angle A=\angle B=\angle C=\angle D={90}^{\circ }$

$\text{A quadrilateral with all its angle 90° is a rectangle}$

$\therefore \text{The quadrilteral ABCD is a rectangle.}$