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2 years ago

Find angle abc (2x+14) (x+7)

2 answers:

7 0

It's a complementary angle, so just solve for x and subtract the CBD from 90,
First, we have to solve for x.
2x + 14 + x + 7 = 90
Combine like terms
3x + 21 = 90
Balance, subtract 21 from each side.
3x = 69
Divide 3 from each side
x = 23.
So know that we know x is 23, we can go about it 2 ways, subtracting the other angle with 90 or just substituting the variable, I'd just substitute the variable for it so just do 23 + 7. That equals 30, angle ABC = 30.

Nata [24]2 years ago

6 0

Angles represented by 2x+14 and x+7 must add up to 90 degrees. Thus,

2x+14 + x+7 = 90, so that

3x + 21 = 90, or 3x = 69, or x = 23.

Then angle ABC is x+7, or 23+7, or 30 degrees.

If that's the case, then angle CBD must be 60 degrees. Is it?
Subst. 23 for x in 2x+14: 2(23)+14 =46+14 = 60 (degrees). YES.

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2 years ago

2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):

zlopas [31]

<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

$A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)$

First pair of opposite sides:

<u>Slope:</u>

$\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}$

Second pair of opposite sides:

<u>Slope:</u>

$\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}$

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

$d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\$

So the diagonals measure the same, therefore this is a rectangle.

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3 years ago

What is the answer to -4+4?

natulia [17]

Answer:

the answer is 0, have a nice day

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2 years ago

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