Question

In the given figure, four rhombuses are built around a square of side 2 cm.

What additional information do you require to construct this figure?

• A. $\angle$ ICB = 60${}^{\circ }$
• B. $\angle$ ICB = 45${}^{\circ }$
• C. $\angle$ ICB = 30${}^{\circ }$
• D. It cannot be determined.

Answer 1

The correct option is B

$\angle$ ICB = 45${}^{\circ }$

Since all 4 angles of a square are right angles, so

$\angle$ ICJ = 90${}^{\circ }$ ___(1)

$\angle$ ICB + $\angle$ ICJ + $\angle$ ICD = 180${}^{\circ }$

Using equation (1), we get

$\angle$ ICB + $\angle$ ICD = 90${}^{\circ }$

2$\angle$ ICB = 90${}^{\circ }$ _____($\angle$ ICB = $\angle$ ICD)

$\angle$ ICB = 45${}^{\circ }$

$\angle$ ICB = $\angle$ ICD = 45${}^{\circ }$