Question

1. ∠abc is a straight angle. find m∠abx and m∠cbx

Explanation:

Step1: Set up equation

Since $\angle ABC$ is a straight - angle, $m\angle ABX+m\angle CBX = 180^{\circ}$. So, $(14x + 70)+(20x+8)=180$.

Step2: Combine like terms

$14x+20x+70 + 8=180$, which simplifies to $34x+78 = 180$.

Step3: Isolate the variable term

Subtract 78 from both sides: $34x=180 - 78$, so $34x = 102$.

Step4: Solve for x

Divide both sides by 34: $x=\frac{102}{34}=3$.

Step5: Find $m\angle ABX$

Substitute $x = 3$ into the expression for $m\angle ABX$: $m\angle ABX=14x + 70=14\times3+70=42 + 70=84^{\circ}$.

Step6: Find $m\angle CBX$

Substitute $x = 3$ into the expression for $m\angle CBX$: $m\angle CBX=20x + 8=20\times3+8=60 + 8=96^{\circ}$.

Answer:

$m\angle ABX = 84^{\circ}$, $m\angle CBX = 96^{\circ}$