Answer:
m∠ABD° = 24°
m∠CBD° = 24°
m∠ABC° = 48°
Step-by-step explanation:
Since [tex]\sf{\overrightarrow{BD}}[/tex] bisects ∠ABC, then it means that ∠ABD + ∠CBD = ∠ABC.
Hence, we can establish the following equality statement:
m∠ABD° = m∠CBD°
Substitute the values for both angles and solve for the value of x:
m∠ABD° = m∠CBD°
3x + 6 = 7x - 18
Subtract 3x from both sides:
3x - 3x + 6 = 7x - 3x - 18
6 = 4x - 18
Add 18 to both sides:
6 + 18 = 4x - 18 + 18
24 = 4x
Divide both sides by 4 to solve for x:
[tex]\large\mathsf{\frac{24}{4}\:=\:\frac{4x}{4}}[/tex]
x = 6
Substitute the value of x = 6 to find the measure of the following angles:
m∠ABD° = 3x + 6 = 3(6) + 6 = 24°
m∠CBD° = 7x - 18 = 7(6) - 18 = 24°
m∠ABC° = m∠ABD° + m∠CBD° = 48°
