Question

Construct a rhombus $ABCD$ where $AC=6cm$ and $BD=7cm.$

Then, $\angle ABD$ is:

• A. $40.7˚$
• B. $42˚$
• C. $45˚$
• D. $60˚$

Answer 1

The correct option is A $40.7˚$

1. Draw a diagonal $AC=6cm$.

2. Draw a perpendicular bisector of $AC$, let the perpendicular bisector and $AC$ intersects at $O$ ($\because$ Diagonals of rhombus intersects at right angle)

3. Taking $O$ as centre and half of the length of another diagonal (i.e $3.5cm$) as radius, mark arc on the perpendicular bisector at both sides of $AC$. Name these intersection points as $B$ and $D$

4. Join $AB,AD,BC,CD$.

5. $ABCD$ is the required rhombus.

6. Measure the $\angle ABD$ which come out to be $40.7˚$