Question

segment and an directions: in the appropriate space example, place all you work for quest 1) 2) (13x - 20)° (7x)° a b d m∠abc = ____° 16 10 19 110

Explanation:

Step1: Use angle - addition postulate

Since $\angle ABC$ and $\angle CBD$ form a linear - pair (a straight line $AD$), $\angle ABC+\angle CBD = 180^{\circ}$. So, $(13x - 20)+7x=180$.

Step2: Combine like terms

Combine the $x$ - terms: $13x+7x-20 = 180$, which simplifies to $20x-20 = 180$.

Step3: Add 20 to both sides

$20x-20 + 20=180 + 20$, resulting in $20x=200$.

Step4: Solve for $x$

Divide both sides by 20: $x=\frac{200}{20}=10$.

Step5: Find the measure of $\angle ABC$

Substitute $x = 10$ into the expression for $\angle ABC$: $\angle ABC=13x - 20$. So, $\angle ABC=13\times10-20=130 - 20 = 110^{\circ}$.

Answer:

$110$