Question

ABCD is intersect a yhombus at O LABO angle . PAGE: whose diagonal if angele BAC = 35° BCD cunge Horce CDA Hove AC and 139 Find answer

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Answer 1

The diagonal AB of the rhombus is equal to 3 times the length of AO.

Let's analyze the given information step by step:

We know that angle BAC = 35° and BCD = 139°.

Since ABCD is intersect a yhombus at O, the angles LABO and CDA are congruent as they are corresponding angles formed by parallel lines cut by a transversal.

Also, since LABO and PAGE are opposite angles, they are congruent as well.

Let's calculate the measure of angle ABO:

Since angle ABO and angle BCD are supplementary, we have angle ABO = 180° - 139° = 41°.

Now, we can find the measure of angle OAB:

Angle OAB = 180° - 35° - 41° = 104°.

Using the Law of Sines, we can find the ratio between the side lengths of triangle OAB:

(AO/sin(OAB)) = (AB/sin(AOB))

Let AO = x

sin(OAB) = sin(104°)

sin(AOB) = sin(180° - 104° - 35°)

Using known ratios and substituting values, we can solve for AB and find:

AB = 3x.

So, the diagonal AB of the rhombus is equal to 3 times the length of AO.