Question

Find the stated lengths and angle measures of rhombus ABCD. Round to the nearest tenth.

Also can you explain how you got the answer?

Answer 1

1. AB = 10 ( as all sides or rhombus are equal )

2. Angle CED = 90° ( in a rhombus diagonals intersect at right angles. )

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Answer 2

The stated lengths and angle measures of rhombus ABCD include the following:

1. AB = 10 units.

2. m∠CED = 90°.

3. m∠BCE = 74°

What is a rhombus?

In Mathematics and Geometry, a rhombus is a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent;

AB = 10 units.

Part 2.

Since a rhombus has two diagonals that bisect each other at right angles (90 degrees), the angle measure of CED is given by;

m∠CED = 90°

Part 3.

The opposite interior angles of a rhombus are congruent and the sum of all the four interior angles is equal to 360 degrees;

m∠BCD ≅ m∠BAD

m∠ABC ≅ m∠ADC

m∠ABC = 2 × 53

m∠ABC = 106°

m∠ABC + m∠ADC + m∠BCD = 360

106 + 106 + m∠BCD = 360

m∠BCD = 148°

m∠BCE = m∠BCD/2

m∠BCE = 148/2

m∠BCE = 74°