Question

I need help solve this

Answer 1

m∠ABC = 95 degrees m∠ABD = 37 degrees m∠DBC = 58 degrees

I don't know how to explain but the someone explained it perfectly and he is correct. :D

Answer 2

m∠ABD = 37°

m∠DBC = 58°

Explanation:

We are given that:

• m∠ABC = 95°
• m∠ABD = (2x + 23)°
• m∠DBC = (9x - 5)°

We can identify from the diagram that:

• m∠ABC = m∠ABD + m∠DBC

We can plug the given values into this equation to solve for x:

95 = (2x + 23) + (9x - 5)

↓ grouping like terms

95 = (2x + 9x) + (23 - 5)

↓ combining like terms

95 = 11x + 18

↓ subtracting 18 from both sides

77 = 11x

↓ dividing both sides by 11

7 = x

Now, we can plug this x-value into each of the angles' definitions to solve for each one's measure:

m∠ABD = (2x + 23)°

m∠ABD = (2(7) + 23)°

m∠ABD = (14 + 23)°

m∠ABD = 37°

m∠DBC = (9x - 5)°

m∠DBC = (9(7) - 5)°

m∠DBC = (63 - 5)°

m∠DBC = 58°

We can check these by plugging them into the equation we constructed from the diagram:

m∠ABC = m∠ABD + m∠DBC

95° ≟ 37° + 58°

95°
`\stackrel{\checkmark}{=}` 95°