When two straight lines intersect, the pairs of nonadjacent angles in opposite posi-tions are known as vertical angles.

If a segment AB is intersected by a transversal labeled t, then ∠1 and ∠3 and ∠2 and ∠4 are vertically angles formed by the transversal t on the segment AB.

Angles ∠1 and ∠2 can be described as adjacent and supplementary angles, so

$m\angle 1+m\angle 2=180^{\circ}$ .

Angles ∠3 and ∠2 can be also described as adjacent and supplementary angles, so

$m\angle 3+m\angle 2=180^{\circ}$ .

Subtract from the first equation the second equation:

$m\angle 1+m\angle 2-(m\angle 3+m\angle 2)=180^{\circ}-180^{\circ},\\ m\angle 1-m\angle 3=0,\\ m\angle 1=m\angle 3$ .

Similarly you can prove that $m\angle 2=m\angle 4$ .

4 0

3 years ago

A savings account compounds interest, at a rate of 25% once a year. Eve puts 500 in the account as the principal. How can eve se

Alekssandra [29.7K]

F(x) = 500(1.25)^x would be the function

8 0

3 years ago

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Rosa and Albert receive the same amount of allowance each week . The table shows what part of their allowance they each spent on

Anettt [7]

1/2 x > 0.4x

where Robert's spending is greater than Rosa's spending.

Allowance of Rosa = Allowance of Robert

let x = allowance

Rosa : video games = 0.4(x) ; pizza = 2/5 (x)
Robert : video games = 1/2 (x) ; pizza = 0.25 (x)

let us assume that their allowance is 100 each week. so, x = 100

Rosa : video games = 0.40(100) = 40
pizza 2/5 (100) = 200/5 = 40
total spending: 40 + 40 = 80

Robert : video games = 1/2 (100) = 50
pizza 0.25 (100) = 25
total spending: 50 + 25 = 75

Spending on video games
Rosa = 40
Robert = 50

Robert spent more of his allowance on video games than Rosa.

1/2 x > 0.4x

7 0

3 years ago