Question

find $m\angle abd$ and $m\angle dbc$. enter deg after any value that is in degrees.
a) $m\angle abd$
$m\angle abd = $
b) $m\angle dbc$
$m\angle dbc = $

Explanation:

Step1: Set up the equation

Since ∠ABD and ∠DBC are supplementary (they form a linear pair), their measures add up to 180 degrees. So we have the equation:
$$(4x + 70) + (5x + 56) = 180$$

Step2: Simplify and solve for x

Combine like terms:
$$9x + 126 = 180$$
Subtract 126 from both sides:
$$9x = 180 - 126$$
$$9x = 54$$
Divide both sides by 9:
$$x = \frac{54}{9}$$
$$x = 6$$

Step3: Find m∠ABD

Substitute x = 6 into the expression for ∠ABD:
$$m\angle ABD = 4x + 70 = 4(6) + 70 = 24 + 70 = 94$$
So \(m\angle ABD = 94\) deg.

Step4: Find m∠DBC

Substitute x = 6 into the expression for ∠DBC:
$$m\angle DBC = 5x + 56 = 5(6) + 56 = 30 + 56 = 86$$
So \(m\angle DBC = 86\) deg.

Answer:

a) \(m\angle ABD = 94\) deg
b) \(m\angle DBC = 86\) deg