Question

1. fill in the blank 2 points use the value of x to find the measure of ∠adb m∠adc = 153° m∠adb =

Explanation:

Step1: Set up equation based on angle - sum

Since $\angle ADC=\angle ADB+\angle BDC$, and $\angle ADC = 153^{\circ}$, $\angle ADB = 7x^{\circ}$, $\angle BDC=(11x + 9)^{\circ}$, we have the equation $7x+(11x + 9)=153$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $(7x+11x)+9 = 153$, which gives $18x+9 = 153$.

Step3: Isolate the variable term

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

Step4: Solve for x

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

Step5: Find the measure of $\angle ADB$

Substitute $x = 8$ into the expression for $\angle ADB$. Since $\angle ADB = 7x^{\circ}$, then $\angle ADB=7\times8^{\circ}=56^{\circ}$.

Answer:

$56^{\circ}$