What are the angle measures of the triangle? (Answer choices in picture)

Mathematics

1 answer:

antiseptic1488 [7]3 years ago

4 0

I would go with 45,45, 90 because first you can eliminate C and D.
C because it is not an equilateral triangle and D because you can figure it out.

Now you have A and B. A 30, 60 90 Degree Triangle would mean that none of the sides are equal (or the legs don't equal the hypotenuse when you put it in Pythagorean form [a²+b²=c²]). However if you translate the problem to answers that are easier to understand: {(7√3 = 12.124)² + 21² = 587.8944 = 14√3} Then you can see, two angles are equal to each other. So the answer is B.

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What is the value of x?

Nikolay [14]

Answer: 7 centimeters

Explanation:

Let triangle ABC and triangle CDE form a bow tie such that
- triangle ABC is smaller than triangle CDE
- Segment AC and segment CD are the north sides
- Segment BC and segment CE are the bottom sides
- AC = 6, CD = 42, CE = 36, BC = x

Since angle ACB and angle ECD are formed by intersecting segment AE and segment BD at point C, they are vertical angles. (See the attached picture) So, angle ACB and angle ECD are congruent.

Moreover when we form our bowtie, point A is in the north side and point E is in the bottom sides and this implies that angle BAC and angle CED are alternate interior angles as shown in the attached figure.

Since it is given in the problem that alternating interior angle are congruent, angle BAC and angle CED are congruent.

Now, we have the following pairs of angles in triangle ABC and triangle CDE that are congruent:

- angle BAC and angle CED
- angle ACB and angle ECD

By AA Similarity theorem, when we have two pairs of congruent angles for two triangles, then the two triangles are similar. So, triangle ABC and triangle CDE are similar.

In similar triangles, the sides that are opposite to the congruent angles are proportional to each other. So,

$\frac{BC}{CD} = \frac{AC}{CE} 


$ (1)

Since $AC = 6, CD = 42, CE = 36, BC = x$ , we can substitute these values to equation (1). So, equation (1) becomes

$\frac{x}{42} = \frac{6}{36}$
$\frac{x}{42} = \frac{1}{6}$ (2)

SInce we are solving for x, we can multiply both sides of equation (2) by the denominator at the left side which is 42 so that

x = 42(1/6)
x = 7 centimeters

8 0

3 years ago

The coefficient of x in the expansion of<br> (x + 3)(x - 1) is

jarptica [38.1K]

waifuhaditallte

Step-by-step explanation:

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3 years ago

Helping my 2nd grader with his math homework and came across this. I don't know Common Core but I can find the sum "the old fash

n200080 [17]

427+316

step one- add 400 and 300=700
step two- take 3 from the 16 and add it to the 27 and add - 27+3+13=43
step three- add 43 and 700

I think that the common core way just adds more steps and makes it more complicated than just adding it regularly, but that's just me.

3 0

3 years ago

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Sheila deposited $1,050.00 into a saving account at her local bank. if the interest rate is 1.5%, then how much will he have aft

Helga [31]

A=p (1+r)^t
A future value?
P present value 1050
r interest rate .015
t time 18/12
A=1,050×(1+0.015)^(18÷12)
A=1,073.71

5 0

4 years ago

786,382 rounded to nearest ten thousand

inna [77]

the answer is 790000.

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3 years ago

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