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asambeis [7]
3 years ago
6

1. Using the drawing, if the measure of angle 2 is 42° and the measure of angle 3 is 52°, what is the measure of angle 6?

Mathematics
2 answers:
Ann [662]3 years ago
4 0

first is 86

we know because of the sum of the interior angles of a triangle being 180, and that 5 + 6 =180

Mazyrski [523]3 years ago
3 0

Answer:  The correct options are (1) (D) 94°  and (2) (D) 15.81.

Step-by-step explanation:  The calculations are as follows:

(1) In the attached figure, given that m∠2 = 42° and m∠3 = 52°.

We are to find the measure of ∠6.

In a triangle, the sum of the measures of two remote interior angles is equal to the measure of the exterior angle.

In the given triangle,  ∠2 and ∠3 are remote interior angles and ∠6 is the exterior angle.

So, we have

m\angle 6=m\angle 2+m\angle 3=42^\circ+52^\circ=94^\circ.

Thus, (D) 94° is the correct option.

(2) Given that the areas of two similar hexagons are related to each other as 5 : 2 and one side of the first hexagon is 25.

We are to find the corresponding side in the other hexagon.

Let, 'a' and 'b' be the lengths of the corresponding sides of the two similar hexagons.

The, the ratios of the area of the hexagons will be a² : b².

So, we have

\dfrac{a^2}{b^2}=\dfrac{5}{2}\\\\\\\Rightarrow \dfrac{25^2}{b^2}=\dfrac{5}{2}\\\\\\\Rightarrow b^2=2\times\dfrac{625}{5}\\\\\\\Rightarrow b^2=250\\\\\Rightarrow b=5\sqrt{10}=15.81.

Thus, the correct option is (D) 15.81.

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One number exceeds another number by 6. One fourth of the sum of the two numbers is two less than the smaller.
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Answer:

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Step-by-step explanation:

let the 2 numbers be x and y , x > y , then

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\frac{1}{4} (x + y) = y - 2 ( multiply both sides by 4 to clear the fraction )

x + y = 4y - 8 ( subtract 4y from both sides )

x - 3y = - 8 → (2)

Substitute x = y + 6 into (2)

y + 6 - 3y = - 8

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y = 7

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x = 7 + 6 = 13

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Step-by-step explanation:

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