Question

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The measurement of an angle is 40°, and the length of a line segment is 8 centimeters.
The number of unique rhombuses that can be constructed using this information is
.

Answer 1

Answer: The answer is only one rhombus can be drawn.

Step-by-step explanation: Given that the measurement of an angle of a rhombus is 40°, and the length of a line segment is 8 centimetres. We are to check how many unique rhombuses can be drawn with this information.

Let us consider a rhombus ABCD with AB = 8 cm and ∠A = 40°.

We know that all the sides of a rhombus are equal, so we have

AB = BC = CD = DA = 8 cm.

Also, the consecutive angles of a rhombus are supplementary, so we have

∠A + ∠B = 180°

implies ∠B = 180° - 40° = 140°.

Therefore, ∠C = 40° and ∠D = 140°.

See the attached picture please.

Thus, only one unique rhombus can be drawn.

Answer 2

Only one unique rhombus can be constructed using the given information.

Explanation:

For better understanding of the solution see the attached figure :

One angle of the rhombus = 40

Let ∠A = 40°

Sum of adjacent angle of rhombus is 180°

∠A + ∠B = 180°

⇒ ∠B = 140°

Now, ∠B + ∠C = 180°

⇒ ∠C = 40°

And, ∠A + ∠D = 180°

⇒ ∠D = 140°

So, all the four angles are fixed.

Now, length of one line segment = 8 cm

But, in a rhombus all the sides are of equal lengths

So, each side is of 8 cm

Now, each side and all the four angle of a rhombus are fixed.

⇒ Only one unique rhombus can be constructed using the given information.