Question

if ∠adc is a straight angle. find m∠bdc. (3x - 25)° (5x + 57)° d find the length of the segment ab if the points given are a (-4,

Explanation:

Step1: Recall straight - angle property

A straight angle measures 180°. So, \((3x - 25)+(9x + 51)=180\).

Step2: Combine like terms

\(3x+9x-25 + 51=180\), which simplifies to \(12x+26 = 180\).

Step3: Isolate the variable term

Subtract 26 from both sides: \(12x=180 - 26\), so \(12x=154\).

Step4: Solve for x

\(x=\frac{154}{12}=\frac{77}{6}\).

Step5: Find the measure of ∠BDC

Substitute \(x = \frac{77}{6}\) into the expression for ∠BDC which is \(3x-25\).
\(m\angle BDC=3\times\frac{77}{6}-25=\frac{77}{2}-25=\frac{77 - 50}{2}=\frac{27}{2}=13.5\).

Answer:

\(13.5^{\circ}\)