Question

sept. 4 unit 1 #10 the student be able to calculate missing angles in a diagram
find ab and bc if ac = 120
a 4x + 6 b 7x + 15 c

Explanation:

Step1: Set up equation based on line - segment addition

Since $AC=AB + BC$ and $AC = 120$, $AB=4x + 6$, $BC=7x + 15$, we have the equation $(4x + 6)+(7x + 15)=120$.

Step2: Combine like - terms

$4x+7x+6 + 15=120$, which simplifies to $11x+21 = 120$.

Step3: Isolate the variable term

Subtract 21 from both sides: $11x=120 - 21$, so $11x=99$.

Step4: Solve for x

Divide both sides by 11: $x=\frac{99}{11}=9$.

Step5: Find AB

Substitute $x = 9$ into the expression for $AB$: $AB=4x + 6=4\times9+6=36 + 6=42$.

Step6: Find BC

Substitute $x = 9$ into the expression for $BC$: $BC=7x + 15=7\times9+15=63+15=78$.

Answer:

$AB = 42$, $BC = 78$