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3 years ago

What type of triangle has an exterior angle that is obtuse at two vertices? Explain your reasoning.

Mathematics

1 answer:

navik [9.2K]3 years ago

5 0

Answer:

A right triangle

Step-by-step explanation:

A right triangle would meet these characteristics. A triangle's inner angles always add up to be 180 degrees. A right triangle has one angle at 90 degrees meaning the other two angles need to be less than 90 degrees and sum up to be 90 degrees. This would indicate that both of these angles' exterior angles would be obtuse because they would be wider than 90 degrees.

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two interior angles of a pentagon measures 112 degrees and 68 degrees and the remaining angles are of the same measures. Find th

jarptica [38.1K]

Answer:

120°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 5 since a pentagon has 5 sides, thus

sum = 180° × 3 = 540°

let x be the measure of the 3 equal angles

Sum the interior angles and equate to 540

112 + 68 + 3x = 540, that is

180 + 3x = 540 ( subtract 180 from both sides )

3x = 360 ( divide both sides by 3 )

x = 120

Hence the measure of each equal interior angle is 120°

6 0

3 years ago

Read 2 more answers

Which of the following is an example of dramatic irony in this scene?

jolli1 [7]

Choice a is correct

3 0

3 years ago

Find the inverse. f(x)= 2x-5/3x+4

zepelin [54]

Answer:

F.MBFFBLKFDKGBKK FGLK doingTDKDT

Step-by-step explanation:

3 0

3 years ago

Every week I buy four 2-litre bottles of lemonade whilst shopping at my local supermarket. Last week the bottles on the shelf we

Mumz [18]

Answer:

40%

Step-by-step explanation:

Every week you he buys 4 number of 2 Litres bottle of lemonade.

Thus, let's say cost of each bottle is X.

This means he total cost is 4X

Now, total litres = 4 × 2 = 8 litres

Thus, cost per litre = 4X/8 = ½X

Now, we are told that Last week the bottles on the shelf were limited edition “2.5 litres for the price of 2 litres” bottles ".

This means that now, it is cheaper.

However, the supermarket also had a “buy 3 bottles, get another one free” offer.

Now since he buys 8 litres weekly, now since it's 2.5 L bottle, he will buy 3 since he will be given 1 free for every 3 he buys.

Thus, total litres he is paying for = 2.5 × 3 = 7.5 litres

Thus, cost per bottle is; 3X

Since he is getting 1 bottle free, then total bottle he gets is; 7.5 L + 2.5 L = 10L

Thus;

cost per litre is now; 3X/10

Difference in costs per litre is;

½X - 3X/10 = X/5

percentage of the cost of four bottles of lemonade lower than usual last week = (X/5)/(½X) × 100% = 2/5 × 100% = 40%

7 0

4 years ago

Solve the equation. Round to the nearest hundredth. Show work.

Elis [28]

Answer:

The value of x = 0.41

Step-by-step explanation:

∵ $6e^{2x}-5e^{x}=6$

Let $e^{x}=y$

∴ $e^{2x}=y^{2}$

∴ 6y² - 5y = 6

∴ 6y² - 5y - 6 = 0 ⇒ factorize

∴ (3y + 2)(2y - 3) = 0

∴ 3y + 2 = 0 ⇒ 3y = -2 ⇒ y = -2/3

∴ 2y - 3 = 0 ⇒ 2y = 3 ⇒ y = 3/2

∵ $y=e^{x}$

∴ $e^{x}=\frac{-2}{3}$ ⇒ refused

( $e^{ax}$ never gives -ve values)

∵ $e^{x}=3/2$ ⇒ insert ln in both sides

∵ $lne^{ax}=axlne=ax$ ⇒ ln(e) = 1

∴ $xlne=ln(3/2)$

∴ x = ln(3/2) = 0.41

6 0

4 years ago

What type of triangle has an exterior angle that is obtuse at two vertices? Explain your reasoning.​

What type of triangle has an exterior angle that is obtuse at two vertices? Explain your reasoning.