Question

find the measures of ∠adb and ∠bdc formed between the escalators. (6x + 10)° 4x° m∠adb = m∠bdc =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $6x + 10=4x$.

Step2: Solve for $x$

Subtract $4x$ from both sides: $6x-4x + 10=4x-4x$, which gives $2x+10 = 0$. Then subtract 10 from both sides: $2x=- 10$. Divide both sides by 2: $x=-5$.

Step3: Find $m\angle ADB$

Substitute $x = - 5$ into the expression for $\angle ADB$ which is $4x$. So, $m\angle ADB=4\times(-5)=-20$. But angles cannot be negative in this context. There is a mistake above. Since $\angle ADB$ and $\angle BDC$ are supplementary (linear - pair), $6x + 10+4x=180$.

Step4: Solve the new equation for $x$

Combine like terms: $10x+10 = 180$. Subtract 10 from both sides: $10x=170$. Divide both sides by 10: $x = 17$.

Step5: Find $m\angle ADB$

Substitute $x = 17$ into the expression for $\angle ADB$ which is $4x$. So, $m\angle ADB=4\times17 = 68$.

Step6: Find $m\angle BDC$

Substitute $x = 17$ into the expression for $\angle BDC$ which is $6x + 10$. So, $m\angle BDC=6\times17+10=102 + 10=112$.

Answer:

$m\angle ADB = 68$
$m\angle BDC = 112$