Question

pls help in geometry for 100 points and state ur reasoning ty!!!!

Answer 1

We know

Diagonals of a rhombus intersect eachother at 90°

Hence

• AB is the hypotenuse of the right angle traingle having opposite angle at intersection of diagonals

$\\ \sf\longmapsto 3x+2x=90°$

$\\ \sf\longmapsto 5x=90°$

$\\ \sf\longmapsto x=18°$

m<ABD=3(18)=54°

Answer 2

Applying the definition of the diagonals of a kite, m∠ABD = 54°.

Diagonals of a Kite

A kite has two unequal diagonals which bisect each other perpendicularly, meaning, the they form right angles at the point of intersection.

Thus:

90° + 2x + 3x = 180° (sum of angles in a triangle)

• Solve for x

90 + 5x = 180

5x = 180 - 90

5x = 90

x = 18

m∠ABD = 3x

• Plug in the value of x

m∠ABD = 3x

m∠ABD = 3(18)

m∠ABD = 54°

Therefore, applying the definition of the diagonals of a kite, m∠ABD = 54°.

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