Question

Construct a rhombus with side of length $5cm$ and an acute angle of ${45}^{\circ }$ .The measure of the obtuse angle of the rhombus is:

• A. ${135}^{\circ }$
• B. ${245}^{\circ }$
• C. ${270}^{\circ }$
• D. ${145}^{\circ }$

Answer 1

The correct option is A ${135}^{\circ }$

$\Rightarrow$ We know that all sides of rhombus are equal.

$\Rightarrow$ Draw a line segment AB = 5cm.

$\Rightarrow$ Construct an angle of ${45}^{\circ }$ at point A.

$\Rightarrow$ Cut off AD = 5cm.

$\Rightarrow$ Take D as a center with radius 5cm, draw an arc.

$\Rightarrow$ Take B as a center with radius 5cm, draw an arc meet previous arc at point C

$\Rightarrow$ Join BC and CD.

$\Rightarrow$ Thus, $ABCD$ is required rhombus.

$\Rightarrow$ Measure an obtuse angle i.e $\angle ADC$ and $\angle ABC$.

$\therefore$ $\angle ADC=\angle ABC={135}^{\circ }$