**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**

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

**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

∴ x + (2y + 4) = 90

∴ x + 2y + 4 = 90

- 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

the sum by 180

∵ ∠CBD = (2y + 4)

∴ (2y + 4) + (3y + x) = 180

- Add like terms

∴ x + 5y + 4 = 180

- Subtract 4 from both sides

∴ **x + 5y = 176 ⇒ (2)**

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

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