Question

use the value of x to find the measure of ∠bdc.
m∠adc = 153°
m∠bdc = type your answer...

Explanation:

Step1: Set up equation based on angle - sum

Since $\angle ADC=\angle ADB+\angle BDC$, we have $7x+(11x + 9)=153$.

Step2: Combine like - terms

Combining the $x$ terms, we get $(7x+11x)+9 = 153$, which simplifies to $18x+9 = 153$.

Step3: Isolate the variable term

Subtract 9 from both sides: $18x+9 - 9=153 - 9$, so $18x = 144$.

Step4: Solve for $x$

Divide both sides by 18: $x=\frac{144}{18}=8$.

Step5: Find $\angle BDC$

Substitute $x = 8$ into the expression for $\angle BDC$. $\angle BDC=11x + 9$. So $\angle BDC=11\times8+9=88 + 9=97^{\circ}$.

Answer:

$97^{\circ}$