Question

Construct a rhombus of side $6cm$ and one diagonal of length $10cm$. The acute angle in the rhombus is equal to:

• A. ${33}^{\circ }$
• B. ${42}^{\circ }$
• C. ${55}^{\circ }$
• D. ${67}^{\circ }$

Answer 1

The correct option is D ${67}^{\circ }$

$\Rightarrow$ We know that all sides of rhombus are equal. We have given side is 6cm and one diagonal is 10cm.

$\Rightarrow$ Draw a line segment PQ = 6cm.

$\Rightarrow$ Take P as a center with radius 6cm then draw an arc.

$\Rightarrow$ Take Q as as a center with radius 10cm then draw an arc meeting previous arc at point R.

$\Rightarrow$ Take P as a center with radius 6cm and draw an arc.

$\Rightarrow$ Take R as a center with radius 6cm and draw an arc meeting previous arc at point S.

$\Rightarrow$ Join PR, QR, RS, PS and QS.

$\Rightarrow$ Thus, PQRS is the required rhombus.

$\Rightarrow$ We to measure angle of acute angle in the rhombus which is $\angle SPQ$ and $\angle SRQ$

$\Rightarrow$ $\angle SPQ=\angle SRQ={67}^{\circ }$