Find the measure of angel 3

Mathematics

1 answer:

Elena-2011 [213]3 years ago

8 0

Answer:

100

Step-by-step explanation:

Remark

If two opposite arcs are given by being opposite vertically opposite angles, then the value of both the vertically opposite angles are equal to

Vertically opposite angle = 1/2 (arc1 + arc2)

Givens

Arc1 = 60

Arc2 = 100

Solution

The red dot angle = 1/2 (60 + 100)

The red dot angle = 1/2(160)

The red dot angle = 80

Because the red dot angle and <3 are on the same line with the same common point, they are supplementary.

<3 and red dot = 180

<3 + 80 = 180 Subtract 80 from both sides

<3 = 180 - 80

<3 = 100

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Find the perimeter of a field that has length 2/x + 1 and width 5/x^2 -1.

Semmy [17]

Answer:

D)4x + 6/(x + 1)(x - 1)

Step-by-step explanation:

A field is basically a rectangle, so to find the perimeter of our field we are using the formula for the perimeter of a rectangle

$p=2(l+w)$

where

$p$ is the perimeter

$l$ is the length

$w$ is the width

We know from our problem that the field has length 2/x + 1 and width 5/x^2 -1, so $l=\frac{2}{x+1}$ and $w=\frac{5}{x^2-1}$ .

Replacing values:

$p=2(l+w)$

$p=2(\frac{2}{x+1} +\frac{5}{x^2-1})$

Notice that the denominator of the second fraction is a difference of squares, so we can factor it using the formula $a^2-b^2=(a+b)(a-b)$ where $a$ is the first term and $b$ is the second term. We can infer that $a=x^2$ and $b=1^2$ . So, $x^2-1=(x+1)(x-1)$ . Replacing that: