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jok3333 [9.3K]
3 years ago
15

What is the measure of ∠C?

Mathematics
1 answer:
tester [92]3 years ago
7 0
The answer to this is 99.

You take all known values and subtract it from 360. 

360-132-39-90=99.
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Solve for x and y<br><br> 2x+7=3y-1
zlopas [31]
To solve for x and y, isolate each variable and simplify your equation:

Solve for x:
2x+7=3y-1 (Subtract 7 on each side)
2x=3y-8 (Divide by 2 on each side)
x=\frac{3y}{2} -4

Solve for y:
2x+7=3y-1
2x+8=3y (Add 1 on each side)
\frac{2x}{3} + \frac{8}{3}=y (Divide by 3)
y=\frac{2x}{3} + \frac{8}{3}

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3 years ago
Applying the the properties of Congruence.
kolbaska11 [484]

Answer:

LM = 35cm and m \angle H = 98^o

Step-by-step explanation:

For this problem, it is critical to understand what the opening statement means.

Quadrilateral GHJK \cong quadrilateral LMNP means that each pair of <u>corresponding sides</u> between shapes are congruent (they have equal length), and each pair of <u>corresponding angles</u> between shapes are congruent (they have equal measure -- or same number of degrees when measured with a protractor).

So, it's important to be able to determine which pairs are the <u>corresponding</u> parts.  When the congruence is given like Quadrilateral GHJK \cong quadrilateral LMNP  the letters are in a particular order.  That order explains the order in which the shape is drawn out, and they put them in the same order for both shapes to mean that those are the letters that correspond with each other.

So, the first letter of each are a corresponding pair, the second letter of each are a corresponding pair, ... etc

In other words, point G and L correspond, point H and K correspond, etc.

<h3><u>Part 1 -- Find LM</u></h3>

To find the corresponding sides, the sides for these shapes are defined by a two adjacent letters (two letters next to each other in the name, or ... as it wraps around the end of the name... the first and last letter).

\overline{GH} \cong \overline{LM}\\ \overline{HJ} \cong \overline{MN} \\\overline{JK} \cong \overline{NP}\\\overline{KG} \cong \overline{PL}

While all of that is true, we only have a few sides with any information in them.  Notice that side GH in the first shape, and sides PL & LM in the second shape are the only sides with anything written.  So, we just need to determine which sides correspond (and thus, are congruent), so that we know how to move forward.  Looking at the list of congruent sides above, we see that  \overline{GH} \cong \overline{LM}

Since the sides (line segments) are congruent, their lengths are equal

GH = LM

...so we can substitute the expressions for each angle into the equation and solve for the unknown value "x"

GH = LM\\(4x+3)=(6x-13)

(4x+3)+13=(6x-13)+13\\4x+16=6x

(4x+16)-4x=(6x)-4x\\16=2x

divide both sides by 2

\frac{16}{2}=\frac{2x}{2}\\8=x

So, to find the length, LM, we just need to look back at the expression for LM:

LM = 6x-13\\LM = 6(8)-13\\LM = 48-13\\LM = 35

remembering that the lengths are measured in centimeters (as indicated on the diagram): LM = 35cm

<h3><u>Part 2 -- Find m∠H</u></h3>

To find the corresponding angles, the angles for these shapes are defined by a single letter, so since the points correspond in order, the names of the shapes tell which angles are congruent.

\angle G \cong \angle L\\\angle H \cong \angle M\\\angle J \cong \angle N\\\angle K \cong \angle P

While all of that is true, we only have a few angles with any information in them.  Notice that ∠H in the first shape, and ∠L & ∠M in the second shape are the only angles with anything written.  So, we just need to determine which angles correspond (and thus, are congruent), so that we know how to move forward.  Looking at the list of congruent angles above, we see that  

\angle H \cong \angle M

Since the angles are congruent, their measures are equal

m\angle H = m\angle M

...so we can substitute the expressions for each angle into the equation and solve for the unknown value "y"

m\angle H = m\angle M\\(9y+17)=(11y-1)

subtract 1 from both sides

(9y+17)+1=(11y-1)+1\\9y+18=11y

subtract 9y from both sides

\\(9y+18)-9y=(11y)-9y\\18=2y

divide both sides by 2

\frac{18}{2}=\frac{2y}{2}\\9=y

So, to find angle H, we just need to look back at the expression for the measure of angle H:

m\angle H = 9y+17\\m\angle H = 9(9)+17\\m\angle H = 81+17\\m\angle H = 98

remembering that the angle is measured in degrees (as indicated on the diagram): m \angle H = 98^o

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2 years ago
A survey of 350 people found 150 like birds. 170 like squirrels and 30 like both animals. How many like neither?
Arada [10]

Answer:

0

Step-by-step explanation:

150 + 170 + 30 = 350

170 + 30 = 200

200 + 150 = 350

Hope this helps! :)

8 0
3 years ago
Felix signs up for a cell phone that his parents require him to pay for. His bill is $46.80. What impact will his cell phone hav
kogti [31]

Answe

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
If this figure is a regular figure? How many degrees does each angle measure?
bearhunter [10]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\frac{(5 - 2) \times 180}{5}  =  \\

\frac{3 \times 18 \times 10}{5}  = 3 \times 18 \times 2 =  \\

54 \times 2 = 108

Thus each angle has a measure of 108° degrees.

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5 0
2 years ago
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