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2 years ago

Plz put the work clearly plzz I really need these

Mathematics

1 answer:

Dmitrij [34]2 years ago

8 0

Answer:

m∠C = 26°

m∠D = 108°

m∠E = 46°

Step-by-step explanation:

Set up the equation adding the expressions together to equal 180 (sum of all angles in a triangle)

(2x) + (x+3) + (5x-7) = 180

Remove the parentheses

2x + x+ 3 + 5x - 7 = 180

Add like terms

8x - 3 -7 = 8x -4 = 180

8x - 4 = 180

Add 4 on each side to cancel it out on the right

8x - 4 = 180

+4 = +4

8x = 184

Divide each side by 8 to get the variable by itself

8/8 =1 184/8 = 23

x = 23

Substitute x in eac expression

2x = 2(23) = 46°

x + 3 = 23 + 3 = 26°

5x - 7 = 5(23) - 7 = 115 -7 = 108

Chek it by adding all the degrees to make sure it equals 180

46 + 26 + 108 = 72 + 108 = 180

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Answer:

Measure of minor angle JOG is $95.5^{\circ}$

Step-by-step explanation:

Consider a circular track of radius 120 yards. Assume that Cherie starts from point J and runs 200 yards up to point G.

$\therefore m JG = 200 yards, JO=120 yards$ .

Now the measure of minor arc is same as measure of central angle. Therefore minor angle is the central angle $\angle JOG = \theta$ .

To calculate the central angle, use the arc length formula as follows.

$Arc\:Length\left(s\right) = r\:\theta$

Where $\theta$ is measured in radian.

Substituting the value,

$200=120\:\theta$

Dividing both side by 120,

$\dfrac{200}{120}=\theta$

Reducing the fraction into lowest form by dividing numerator and denominator by 40.

$\therefore \dfrac{5}{3}=\theta$

Therefore value of central angle is $\angle JOG = \theta=\left(\dfrac{5}{3}\right)^{c}$ , since angle is in radian

Now convert radian into degree by using following formula,

$1^{c}=\left(\dfrac{180}{\pi}\right)^{\circ}$

So multiplying $\theta$ with $\left(\dfrac{180}{\pi}\right)^{\circ}$ to convert it into degree.

$\left(\dfrac{5}{3}\right)^{c}=\left(\dfrac{5}{3}\right) \times \left(\dfrac{180}{\pi}\right)^{\circ}$

Simplifying,

$\therefore \theta = 95.49^{circ}$

So to nearest tenth, $\angle JOG=95.5^{circ}$

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