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marissa [1.9K]
3 years ago
14

A triangle has angles measuring 2x°, x° and x°. Write an equation that can be solved to find the value of x. Then, find the meas

ure of each angle, in degrees.
Mathematics
1 answer:
Readme [11.4K]3 years ago
3 0

Answer:

The three angles of a triangles are 90° , 45°, 45°

∠A =  90° , ∠B = 45° and ∠C = 45°

Step-by-step explanation:

<u>Explanation</u>:-

<u><em>Step(i)</em></u>:-

The sum of measures of three angles of any triangle is equal to 180°

<em>Let A , B , C be the  angles of the triangle.</em>

<em>∠A +∠B +∠C = 180°</em>

Given data a triangle has angles measuring 2x°, x° and x°

<em>2x°+ x° + x° = 180°</em>

<em>4x° = 180</em>

<em>x° = </em>\frac{180}{4} = 45<em />

x = 45°

<em><u>Step (ii)</u></em><u>:-</u>

Given data  2x = 2 × 45 = 90°

                      x = 45°

and                x = 45°

The three angles of a triangles are 90° , 45°, 45°

∠A =  90° , ∠B = 45° and ∠C = 45°

<u>Final answer</u>:-

The three angles of a triangles are 90° , 45°, 45°

∠A =  90° , ∠B = 45° and ∠C = 45°

<u></u>

<u></u>

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The length of a 200 square foot rectangular vegetable garden is 4feet less than twice the width. Find the length and width of th
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Step-by-step explanation:

let the length of the field be x ft

and the width be y ft

as per the condition given in problem

x=2y-4   -----------(A)

Also the area is given as 200 sqft

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Hence from A we get

y(2y-4)=200

taking 2 as GCF out

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Dividing both sides by 2 we get

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subtracting 100 from both sides

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Now we solve the above equation with the help of Quadratic formula which is given in the image attached with this for any equation in form

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Here in our case

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Putting those values in the formula and solving them for y

y=\frac{-(-2)+\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}

y=\frac{-(-2)-\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}

Solving first

y=\frac{2+\sqrt{4+400}{2}

y=\frac{2+\sqrt{404}{2}

y=\frac{2+20.099}{2}

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Solving second one

y=\frac{-(-2)-\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}

y=\frac{2-\sqrt{4+400}{2}

y=\frac{2-\sqrt{404}{2}

y=\frac{2-20.099}{2}

y=\frac{-18.99}{2}

y=-9.045

Which is wrong as the width can not be in negative

Our width of the field is

y=11.099

Hence the length will be

x=2y-4

x=2(11.049)-4

x=22.099-4

x=18.099

Hence our length x and width y :

Length = 18.099 ft

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