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White raven [17]
2 years ago
5

Angle Sum Theorem what is y

Mathematics
2 answers:
Mamont248 [21]2 years ago
6 0

9514 1404 393

Answer:

  y = 90°

Step-by-step explanation:

The angle sum theorem tells you the sum of angles in a triangle is 180°. You also know that the sum of the angles of a linear pair is 180°.

Let z represent the measure of the unmarked interior angle at the the lower left of the triangle shown. Then we have ...

  110° + z = 180° . . . . angles of a linear pair are supplementary

  z +2x +70° = 180° . . . Angle Sum theorem

Then we can write ...

  110° +z = z +2x +70°

  110° = 2x +70° . . . . . the exterior angle is equal to the sum of the remote interior angles.

  40° = 2x . . . . . . . . . subtract 70°

  20° = x

Similarly, we have ...

  110° = x + y . . . . . . . exterior angle = sum of remote interior angles

  110° -20° = y = 90° . . . . subtract x=20°

_____

<em>Additional comment</em>

You may be able to get there a lot faster by recognizing z = 180° -110° = 70°, hence the triangle is isosceles. The angle bisector creating angles x is then also an altitude, hence y = 90°.

zaharov [31]2 years ago
5 0

Answer:

y = 90°

Step-by-step explanation:

The angle sum theorem tells you the sum of angles in a triangle is 180°. You also know that the sum of the angles of a linear pair is 180°.

Let z represent the measure of the unmarked interior angle at the the lower left of the triangle shown. Then we have ...

110° + z = 180°. are supplementary angles of a linear pair

z +2x +70° = 180°...Angle Sum theorem

Then we can write ...

110° +z = z +2x +70°

110° 2x +70°..... the exterior angle is equal to the sum of the remote interior angles.

40° = 2x......... subtract 70°

20° = x

Similarly, we have ...

110° = x+y....... exterior angle = sum of remote interior angles

40° = 2x.

20° = x

Similarly, we have ...

110° = x + y ....... exterior angle = sum of remote interior angles

110° -20° y = 90°. .... subtract x=20°

Additional comment

You may be able to get there a lot faster by recognizing z = 180° -110° = 70°, hence the triangle is isosceles. The angle bisector creating angles x is then also an altitude, hence y = 90°.

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alexandr402 [8]

Answer: Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

Step-by-step explanation:

Hope this is what you were looking for

6 0
3 years ago
A bus company took a tour bus on a ferry when there were 30 people aboard. The ferry charged the bus company $180. The following
OLEGan [10]
Problem: A bus company took a tour bus on the ferry when there were 30 people aboard. The ferry charged the bus company $180. The following week, the bus had 50 people on board and the ferry charged them $220. How much is the "base rate" for the empty bus? How much does each person cost? Show this using y = mx + b form.

Solution:
Let x = the number of people on the bus
Let y = the total cost for the bus with its passengers to use the ferry.

Then, when there are 30 people on the bus (x = 30), the cost was $180 (y = 180). This means the point (x, y) = (30, 180).
Also, when there were 50 people on the bus, the cost was $220. So that is the point (50, 220).

You see - we have two points and so we can write the equation of a line that goes through those points. The first thing we have to do is find the slope.

The slope of the line joining two points is the rise divided by the run. That means

m = (y2 - y1) / (x2 - x1)

So we put in the values of (30, 180) and (50, 220):

m = (220 - 180) / (50 - 30)
m = 40 / 20
m = 2.

The slope is 2. Now we can write it in the form y = mx + b, using 2 for m:

y = 2x + b.

This equation connects both points, so that means it goes through those points. We want to know "b" next, so we can now substitute in either point for the x and the y. I will substitute in x = 50 and y = 220:

220 = 2(50) + b
220 = 100 + b
b + 100 = 220
b = 120.

Now I know the b and the m, so I can finally write the full y=mx + b form of the equation:

y = 2x + 120.

For the other questions, I can look at the equation I got. The y-intercept (b value) is $120. That means that we are adding $120 on to the price all the time. That's the price for the empty bus. The 2x means to multiply the number of people by two and add this to the $120. So each person is $2.

Here's an example: if you had just 10 people on the bus, you'd pay $120 for the empty bus and $2 for each person. That's $20 for the people and $120 for the bus. That total is $140. Let's see if (10, 140) works in the equation we got:

y = 2x + 120
140 ?=? 2(10) + 120
140 ?=? 20 + 120
yes. 140 = 140. It does work.

Now you try it with your question.
5 0
3 years ago
A population has groups that have a small amount of variation within them, but large variation among or between the groups thems
Sauron [17]

Answer:

B. stratified.

Step-by-step explanation:

If a population is composed by identifiable groups or strata, with large variations between groups, the stratified sampling should be applied in order to comprehend and represent all of the different groups in the sampling process.

Therefore, the answer is  alternative B. stratified.

6 0
3 years ago
George walked at a rate of 1/3 miles every 20 minutes. What was his walking rate in miles per hour? SHOW YOUR WORK!
goblinko [34]

HIS walking rate was 1 mile per hour  because 20min times 3 is 1 hour, and 1/3 times 3 is 1 mile   thus 1mph     if can plz mark brainliest

7 0
3 years ago
Which set of statements would describe a parallelogram that can always be classified as a rhombus? I. Diagonals are perpendicula
trasher [3.6K]

Answer:

1. I, II,

Step-by-step explanation:

<em>I. Diagonals are perpendicular bisectors of each other  </em>

Yes, because 4 sides are congruent so it makes the two diagonals perpendicular bisectors

<em>II. Diagonals bisect the angles from which they are drawn </em>

Yes, That is the property of the diagonal!

<em> III. Diagonals form four congruent isosceles right triangles. </em>

No, only two pairs of right triangles are congruent and sometime the side of each pair are different to each other.

Hence, we choose I and II

4 0
3 years ago
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