karlybel08
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PLEASE HELP IM BEGGING AND ILL MARK BRAINLIEST
In the figure shown, m∠ABD=8x−28 and m∠DBC=4x+10.

What is the measure of ∠DBC?

Enter your answer in the box.
m∠DBC=_____

PLEASE HELP IM BEGGING AND ILL MARK BRAINLIEST In the figure shown mABD8x28 and mDBC4x10 What is the measure of DBC Enter your answer in the box mDBC class=

Respuesta :

semsee45

Answer:

m∠DBC = 46°

Step-by-step explanation:

Given:

  • m∠ABD = 8x - 28
  • m∠DBC = 4x + 10

From inspection of the given diagram, m∠ABC is a right angle.

Therefore, the sum of the two given angles is 90°:

⇒ m∠ABD + m∠DBC = 90°

⇒ (8x - 28) + (4x + 10) = 90

⇒ 8x - 28 + 4x + 10 = 90

⇒ 8x + 4x - 28 + 10 = 90

⇒ 12x - 18 = 90

⇒ 12x - 18 + 18 = 90 + 18

⇒ 12x = 108

⇒ 12x ÷ 12 = 108 ÷ 12

⇒ x = 9

Substitute the found value of x into the expression for m∠DBC:

⇒ m∠DBC = 4x + 10

⇒ m∠DBC = 4(9) + 10

⇒ m∠DBC = 36 + 10

⇒ m∠DBC = 46°

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