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velikii [3]
2 years ago
13

Triangles triangle ABC and triangle DEF are similar. Find the angles of these triangles if Mesurements of angle A=100 degrees, a

nd mesurments of angle B=30 degrees.
Mathematics
1 answer:
beks73 [17]2 years ago
3 0

Answer:

<D = 100

<E =30

<F =50

Step-by-step explanation

Given that triangles triangle ABC and triangle DEF are similar, this means that their angles are congruent i.e

<A = <D

<B = <E

<C = <F

Given

<A = 100 then <D = 100

<B = 30°, then <E = 30°

To get <F, we will use the expression

<D+<E+<F = 180 (sum of angles in a triangle is 180°)

100+30+<F = 180

130+<F = 180

<F = 180-130

<F = 50°

Hence the measure of <F is 50°

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Answer:

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Step-by-step explanation:

Let <em>x </em>represent one-dollar bills and <em>y </em>represent two-dollar bills.

He has a total of 49 bills. Therefore:

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The total amount of money James has is 66. <em>x</em> is worth one dollar, while <em>y</em> is worth two dollars. Therefore:

1x+2y=66\\x+2y=66

We have a system of equations. Solve by substitution:

x+2y=66\\x+y=49\\x=49-y\\(49-y)+2y=66\\y=17\\x=49-17=32

Therefore, James has 32 one-dollar bills and 17 two-dollar bills.

Checking:

32(1)+17(2)\stackrel{?}{=}66\\32(1)+17(2)\stackrel{\checkmark}{=}66\\\\32+17\stackrel{?}{=}49\\49\stackrel{\checkmark}{=}49

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