Question

Find the measure of ABD and DBC given ABC = 77°

Answer 1

• 
  `∠ABD = 42°`
• 
  `∠DBC = 35°`

Given :

• ∠ABC = 77°

To find :

• The measure of ∠ABD and ∠DBC

Solution :

ATQ,

• ∠ABD + ∠DBC = ∠ABC
• 4x - 2 + 3x + 2 = 77°
• 4x + 3x - 2 + 2 = 77°
• 7x = 77°
• x = 77°/7
• x = 11°

Thus,

• ∠ABD = 4*11° - 2 = (44 - 2)° = 42°
• ∠DBC = 3*11° + 2 = (33 + 2)° = 35°

Answer 2

m ∠ABD = 42°

m ∠DBC = 35°

Explanation:

Given:

• m ∠ABD = 4x - 2
• m ∠DBC = 3x + 2
• m ∠ABC = 77°

To find:

• m ∠ABD
• m ∠DBC

Solution:

Since m ∠ABC is the sum of m ∠ABD and m ∠DBC.

So, we can set up equation as:

m ∠ABC = ∠ABD + m ∠DBC

Substitute the given value:

77 = 4x - 2 + 3x + 2

Simplify like terms:

77 = 7x

Divide both sides by 7.

`\sf (77 )/(7) =( 7x )/(7)`

x = 11

Now, we can find the measure of m ∠ABD and m ∠DBC by substituting value of x.

So,

m ∠ABD = 4 × 11 - 2 = 44 - 2 = 42°

m ∠DBC = 3 × 11 + 2 = 33 + 2 = 35°

Therefore, the measure of:

• m ∠ABD = 42°
• m ∠DBC = 35°