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3 years ago

Find the measures of the missing angles:

Mathematics

1 answer:

Illusion [34]3 years ago

6 0

Answer:

m<1 = 70

m<2 = 110

m<3 = 82

Step-by-step explanation:

<1:

x + 75 + 35 = 180

x + 110 = 180

x = 70

<2:

<1 + x = 180

70 + x = 180

x = 110

<3:

The blank angle is 70 (b/c of 180 - 110) and vertical angles with <1

x + 70 + 28 = 180

x + 98 = 180

x = 82

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4 years ago

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3 years ago

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3 years ago

Your third-grade classroom has 32 boys and girls. Two-thirds of the boys and three-fourths of the girls are going on a field tri

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Answer: The ratio of boys to girls would be 3 : 5 .

Step-by-step explanation:

Since we have given that

Number of boys and girls = 32

Fraction of boys are going on a field trip = $\dfrac{2}{3}$

Fraction of girls are going on a field trip = $\dfrac{3}{4}$

Number of children left = 9

Let the number of boys be 'b'.

Let the number of girls be 'g'.

According to question, it becomes ,

$b+g=32------------(1)\\\\32-9=\dfrac{2}{3}b+\dfrac{3}{4}g\\\\23=\dfrac{2b}{3}+\dfrac{3g}{4}-------------(2)$

From eq(1), we get that g = 32-b

So, it becomes,

$\dfrac{2}{3}b+\dfrac{3}{4}(32-b)=23\\\\\dfrac{2}{3}b+24-\dfrac{3}{4}b=23\\\\\dfrac{2}{3}b-\dfrac{3}{4}b=23-24=-1\\\\\dfrac{8b-9b}{12}=-1\\\\\dfrac{-b}{12}=-1\\\\b=-1\times -12\\\\b=12$

so, number of girls would be 32 - b = 32 - 12 = 20

So, Ratio of boys to girls in class would be 12 : 20 = 3 : 5.

Therefore, the ratio of boys to girls would be 3 : 5 .

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4 years ago