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DiKsa [7]
3 years ago
8

Two consecutive integers have a sum of 153. find the integers.

Mathematics
1 answer:
Natasha2012 [34]3 years ago
6 0
X = first integer
x + 1 = second consecutive integer

x + (x + 1) = 153..combine like terms
2x + 1 = 153
2x = 153 - 1
2x = 152
x = 152/2
x = 76

x + 1 = 76 + 1 = 77

so ur numbers are : 76 and 77...and u will find that when added equal 153.
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What is the solution to this equation?
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Angles ∠ABC= x and ∠CBD=(2y+4) are complementary. ∠CBD and ∠DBE=(3y+x) are supplementary.
Basile [38]

The missing question is find x , y and the measure of each angle

The values of x and y are x = 28 and y = 30

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Step-by-step explanation:

Let us revise the meaning of complementary angles and supplementary angles

  • Two angles are complementary if their sum is 90°
  • Two angles are supplementary if their sum is 180°

∵ ∠ABC = x

∵ ∠CBD = 2y + 4

∵ ∠ABC and ∠CBD are complementary

- That means their sum is 90°, add their values and equate

   the sum by 90

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- Subtract 4 from both sides

∴ x + 2y = 86 ⇒ (1)

∵ ∠DBE = (3y + x)

∵ ∠CBD and ∠DBE are supplementary

- That means their sum is 180°, add their values and equate

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- Add like terms

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- Subtract 4 from both sides

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Now we have a system of equations to solve them

Subtract equation (1) from equation (2) to eliminate x

∵ 3y = 90

- Divide both sides by 3

∴ y = 30

- Substitute the value of y in equation (1) to find x

∵ x + 2(30) = 86

∴ x + 60 = 86

- Subtract 60 from both sides

∴ x = 26

∵ ∠ABC = x

∴ The measure of angle ABC is 26°

∵ ∠CBD = 2y + 4

∴ ∠CBD = 2(30) + 4 = 60 + 4 = 64°

∴ The measure of angle CBD is 64°

∵ ∠DBE = 3y + x

∴ ∠DBE = 3(30) + 26 = 90 + 26 = 116°

∴ The measure of angle DBE is 116°

The values of x and y are x = 28 and y = 30

The measures of ∠ABC is 26°, ∠CBD is 64° and ∠DBE is 116°

Learn more:

You can learn more about the complementary angles and supplementary angles in brainly.com/question/10483199

#LearnwithBrainly

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