If the product of the present age of father and his daughter is 430 and the age of father was 4 times as old as his daughter is now, then the present age of father is 43 and the present age of daughter is 10.

Given that the product of the present age of father and his daughter is 430 and the age of father was 4 times as old as his daughter is now.

We are required to find the present age of the father and daughter.

Suppose the present age of the father is x.

Suppose the present age of his daughter is y.

We are given product of present ages be 430.

xy=430----------1

y=430/x

According to question,

x-3=4y

Put the value of y=430/x.

x-3=4*430/x

$x^{2}$ -3x=1720

$x^{2} -3x-1720=0$

x=(3± $\sqrt{3^{2}-4*1*(-1720) }$ )/2*1

x=3± $\sqrt{6889}$ )/2

x=(3±83)/2

x=(3+83)/2

(Ignoring the negative value because the age cannot be negative as it is coming before the greater number)

x=43

y=430/x

y=430/43

y=10

Hence if the product of the present age of father and his daughter is 430 and the age of father was 4 times as old as his daughter is now, then the present age of father is 43 and the present age of daughter is 10.

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Given: <2 and <4 are vertical angles.

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<h2>Explanation:</h2><h2 />

Hello! Remember you have to write complete questions in order to get good and exact answers. Here I could help you in a general way. Vertical Angles are those angles on opposite sides of intersecting lines They takes this name because they have the same vertex, or corner, at the intersection.

Vertical angles are always congruent, so this implies that they always have the same measure. From the figure below, we know that ∠1 and ∠3 are vertical and ∠2 and ∠4 are also vertical, therefore:

∠2 ≅ ∠4

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