Question

using the following diagram, find m∠abc and m∠cbd. (14x - 6.5)° (7x + 8)° a b d m∠abc = ______ m∠cbd = ______ blank 1: blank 2:

Explanation:

Step1: Set up equation using linear - pair property

Since $\angle ABC$ and $\angle CBD$ form a linear - pair, their sum is $180^{\circ}$. So, $(14x - 6.5)+(7x + 8)=180$.

Step2: Combine like terms

$14x+7x-6.5 + 8=180$, which simplifies to $21x+1.5 = 180$.

Step3: Solve for $x$

Subtract $1.5$ from both sides: $21x=180 - 1.5=178.5$. Then divide both sides by $21$: $x=\frac{178.5}{21}=8.5$.

Step4: Find $m\angle ABC$

Substitute $x = 8.5$ into the expression for $\angle ABC$: $m\angle ABC=14x-6.5=14\times8.5-6.5=119 - 6.5 = 112.5^{\circ}$.

Step5: Find $m\angle CBD$

Substitute $x = 8.5$ into the expression for $\angle CBD$: $m\angle CBD=7x + 8=7\times8.5+8=59.5+8 = 67.5^{\circ}$.

Answer:

$m\angle ABC = 112.5$
$m\angle CBD = 67.5$