Question

apply: finding unknown angle measures
angle dba and angle dbc are shown.
find the measure of each angle.
click or tap the correct measure from each drop - down menu.
the measure of ∠dba is choose
the measure of ∠dbc is choose
image of a straight line ac with point b on it, and a ray bd forming angles ∠dba = (8x)° and ∠dbc = (100 + 2x)°

Explanation:

Step1: Identify the angle relationship

Angles ∠DBA and ∠DBC are supplementary (they form a linear pair), so their sum is \(180^\circ\). Thus, \(8x + (100 + 2x)=180\).

Step2: Solve for \(x\)

Combine like terms: \(10x + 100 = 180\). Subtract 100 from both sides: \(10x = 80\). Divide by 10: \(x = 8\).

Step3: Find ∠DBA

Substitute \(x = 8\) into \(8x\): \(8\times8 = 64^\circ\).

Step4: Find ∠DBC

Substitute \(x = 8\) into \(100 + 2x\): \(100 + 2\times8 = 100 + 16 = 116^\circ\).

Answer:

The measure of ∠DBA is \(64^\circ\).
The measure of ∠DBC is \(116^\circ\).