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3 years ago

8

Solve for x and y then find the measurement of each angle

1 answer:

nevsk [136]3 years ago

3 0

Answer:

x = 10

y = 40

Step-by-step explanation:

DE is a straight line so the sum of angles DBA and ABE is equal to 180

13x - 18 + 5x + 18 = 180 add like terms

18x = 180 divide both sides by 18

x = 10

Same rule applies when calculating value of y

3y - 52 + 2y + 32 = 180 add like terms

5y - 20 = 180 add 20 to both sides

5y = 200 divide both sides by 5

y = 40

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Hi there! :)

Answer:

$\huge\boxed{n = -2}$

5n + 6 = -3n - 10

Solve for n:

Add 3n to both sides:

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8n + 6 = -10

Subtract 6 from both sides:

8n + 6 - 6 = -10 - 6

8n = -16

Divide both sides by 8:

8n/8 = -16/8

n = -2.

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Three consecutive odd integers have a sum of 27. Find the integers.

jek_recluse [69]

$\sf \bf {\boxed {\mathbb {GIVEN:}}}$

Sum of three consecutive odd integers = $27$

$\sf \bf {\boxed {\mathbb {TO\:FIND:}}}$

The values of the three integers.

$\sf \bf {\boxed {\mathbb {SOLUTION:}}}$

$\sf\purple{The\:three\:consecutive \:odd\:integers\:are\:7,\:9\:and\:11.}$

$\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}$

Let us assume the three consecutive odd integers to be $x$ , $(x+2)$ and $(x+4)$ .

As per the condition, we have

$Sum \: \: of \: \: the \: \: three \: \: consecutive \: \: odd \: \: integers = 27$

$➺ \: x + (x + 2) + (x + 4) = 27$

$➺ \: x + x + 2 + x + 4 = 27$

Now, collect the like terms.

$➺ \: (x + x + x) + (2 + 4) = 27$

$➺ \: 3x + 6 = 27$

$➺ \: 3x = 27 - 6$

$➺ \: 3x = 21$

$➺ \: x = \frac{21}{3} \\$

$➺ \: x = 7$

Therefore, the three consecutive odd integers whose sum is $27$ are $\boxed{ 7 }$ , $\boxed{ 9 }$ and $\boxed{ 11 }$ respectively.

$\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}$

$⇢ 7 + 9 + 11 = 27$

$⇢ 27 = 27$

⇢ L. H. S. = R. H. S.

$\sf\blue{Hence\:verified.}$

$\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}$

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