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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