Help pls not graded test

Mathematics

1 answer:

Arte-miy333 [17]1 year ago

3 0

The missing angle of the given triangle is 59°.

What is vertically opposite angles?

Angles that are vertically opposed to one another are always equal to one another. A vertical angle and the angle to which it is next are also supplementary angles; that is, they sum up to 180 degrees. As an illustration, if two lines connect to form an angle, say X=45°, then the angle's opposite angle is also 45°.

Here consider angle with 31° and 49° triangle is 1. We know that sum of all angles in triangle is add upto 180°. Then,

⇒ 49°+31°+x = 180°

⇒ 80° + x= 180°

⇒x= 180°-80°=100°

Then unknown angle in triangle 1 ia 100°.

Now according to the vertically opposite angle theorem , opposite angles are equal to each other. Then ,

In triangle 2 angle is 100° and 21°. Then missing angle is,

⇒ 100°+21°+missing angle =180°

⇒Missing angle = 180°-100°-21°

⇒Missing angle = 59°

Therefore the answer is 59°.

To learn more about Vertical angle ,

brainly.com/question/18450499

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elena-14-01-66 [18.8K]

Answer:

x ≈ 2.3 cm

Step-by-step explanation:

Using the cosine ratio in the right triangle

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Four circles of unit radius are drawn with centers $(1,0)$, $(-1,0)$, $(0,1)$, and $(0,-1)$. a circle with radius 2 is drawn wit

Reika [66]

Check the picture 1.

The regions contained in an odd number of these 5 circles are

the pink colored region, contained only in the circle with radius 2,

and the yellow regions, each contained in the intersection of 2 small circles and the third large circle.

So what we need to determine is the "area pink + area yellow".

Consider the second picture.

Let A2 be the area of the right isosceles triangle, and A1 be half of the yellow region.

the region A2 + A1 is called a sector, and it is 1/4 of the area of a unit circle.

$A1=A_{sector}-A2= \frac{1}{4} \pi r^2- \frac{1}{2}.1.1= \frac{1}{4} \pi 1^2- \frac{1}{2}= \frac{1}{4}\pi- \frac{1}{2}$

Thus, the overall yellow region is $8A1=8(\frac{1}{4}\pi- \frac{1}{2})=2\pi-4$

The purple area is:

Area of large circle - 4*(Area of 1 small circle) + yellow region.

(because subtracting all 4 small circles means that each of the 4 separate yellow regions have been subtracted twice)

$A_{purple}=\pi.2^2-4(\pi.1^2)+2\pi-4=4\pi-4\pi+2\pi-4=2\pi-4$

Finally, the total area is : $2\pi-4+2\pi-4=4\pi-8$ (units squared)

Answer: $6\pi-8$ square units